LMFDB - Embedded newform 841.2.e.k.270.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			270.1
Character	$\chi$	$=$	841.270
Dual form			841.2.e.k.651.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04749 - 2.17513i) q^{2} +(1.88751 - 1.50524i) q^{3} +(-2.38699 + 2.99318i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-5.25123 - 2.52886i) q^{6} +(-1.76350 - 2.21135i) q^{7} +(4.30354 + 0.982255i) q^{8} +(0.629384 - 2.75751i) q^{9} +O(q^{10})$	\(q+(-1.04749 - 2.17513i) q^{2} +(1.88751 - 1.50524i) q^{3} +(-2.38699 + 2.99318i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-5.25123 - 2.52886i) q^{6} +(-1.76350 - 2.21135i) q^{7} +(4.30354 + 0.982255i) q^{8} +(0.629384 - 2.75751i) q^{9} +(1.88751 + 1.50524i) q^{10} +(0.403828 - 0.0921712i) q^{11} +9.24264i q^{12} +(-0.851905 - 3.73244i) q^{13} +(-2.96274 + 6.15220i) q^{14} +(-1.04749 + 2.17513i) q^{15} +(-0.667563 - 2.92478i) q^{16} -0.828427i q^{17} +(-6.65722 + 1.51947i) q^{18} +(-4.69099 - 3.74094i) q^{19} +(0.851905 - 3.73244i) q^{20} +(-6.65722 - 1.51947i) q^{21} +(-0.623490 - 0.781831i) q^{22} +(-3.29471 - 1.58665i) q^{23} +(9.60149 - 4.62384i) q^{24} +(-2.49396 + 3.12733i) q^{25} +(-7.22619 + 5.76269i) q^{26} +(0.179721 + 0.373194i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(4.36967 + 9.07372i) q^{31} +(1.23982 - 0.988722i) q^{32} +(0.623490 - 0.781831i) q^{33} +(-1.80194 + 0.867767i) q^{34} +(2.54832 + 1.22721i) q^{35} +(6.75141 + 8.46601i) q^{36} +(3.89971 + 0.890084i) q^{37} +(-3.22328 + 14.1221i) q^{38} +(-7.22619 - 5.76269i) q^{39} +(-4.30354 + 0.982255i) q^{40} -4.48528i q^{41} +(3.66832 + 16.0720i) q^{42} +(-1.55581 + 3.23068i) q^{43} +(-0.688047 + 1.42874i) q^{44} +(0.629384 + 2.75751i) q^{45} +8.82843i q^{46} +(-3.16134 + 0.721555i) q^{47} +(-5.66252 - 4.51571i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(9.41474 + 2.14885i) q^{50} +(-1.24698 - 1.56366i) q^{51} +(13.2054 + 6.35937i) q^{52} +(-8.54594 + 4.11551i) q^{53} +(0.623490 - 0.781831i) q^{54} +(-0.323845 + 0.258258i) q^{55} +(-5.41716 - 11.2488i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(-4.01023 - 8.32733i) q^{60} +(-3.77502 + 3.01048i) q^{61} +(15.1593 - 19.0092i) q^{62} +(-7.20775 + 3.47107i) q^{63} +(-8.85511 - 4.26439i) q^{64} +(2.38699 + 2.99318i) q^{65} +(-2.35368 - 0.537213i) q^{66} +(1.25877 - 5.51503i) q^{67} +(2.47964 + 1.97744i) q^{68} +(-8.60708 + 1.96451i) q^{69} -6.82843i q^{70} +(-1.96451 - 8.60708i) q^{71} +(5.41716 - 11.2488i) q^{72} +(1.73553 - 3.60388i) q^{73} +(-2.14885 - 9.41474i) q^{74} +9.65685i q^{75} +(22.3946 - 5.11143i) q^{76} +(-0.915973 - 0.730464i) q^{77} +(-4.96527 + 21.7543i) q^{78} +(-2.35368 - 0.537213i) q^{79} +(1.87047 + 2.34549i) q^{80} +(8.54594 + 4.11551i) q^{81} +(-9.75608 + 4.69828i) q^{82} +(4.77397 - 5.98637i) q^{83} +(20.4387 - 16.2994i) q^{84} +(0.359441 + 0.746387i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(-5.41716 - 11.2488i) q^{89} +(5.33868 - 4.25745i) q^{90} +(-6.75141 + 8.46601i) q^{91} +(12.6136 - 6.07437i) q^{92} +(21.9059 + 10.5493i) q^{93} +(4.88094 + 6.12051i) q^{94} +(5.84957 + 1.33513i) q^{95} +(0.851905 - 3.73244i) q^{96} +(3.50673 + 2.79653i) q^{97} +(2.35368 - 0.537213i) q^{98} -1.17157i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.04749	−	2.17513i	−0.740686	−	1.53805i	−0.839753	−	0.542969i	$-0.817300\pi$
$2$	−1.04749	−	2.17513i	−0.740686	−	1.53805i	0.0990667	−	0.995081i	$-0.468414\pi$
$3$	1.88751	−	1.50524i	1.08975	−	0.869049i	0.0977437	−	0.995212i	$-0.468837\pi$
$3$	1.88751	−	1.50524i	1.08975	−	0.869049i	0.992010	+	0.126162i	$0.0402660\pi$
$4$	−2.38699	+	2.99318i	−1.19349	+	1.49659i
$5$	−0.900969	+	0.433884i	−0.402926	+	0.194039i	−0.624360	−	0.781136i	$-0.714640\pi$
$5$	−0.900969	+	0.433884i	−0.402926	+	0.194039i	0.221435	+	0.975175i	$0.428926\pi$
$6$	−5.25123	−	2.52886i	−2.14381	−	1.03240i
$7$	−1.76350	−	2.21135i	−0.666539	−	0.835813i	0.327499	−	0.944852i	$-0.393794\pi$
$7$	−1.76350	−	2.21135i	−0.666539	−	0.835813i	−0.994038	+	0.109039i	$0.965223\pi$
$8$	4.30354	+	0.982255i	1.52153	+	0.347280i
$9$	0.629384	−	2.75751i	0.209795	−	0.919171i
$10$	1.88751	+	1.50524i	0.596882	+	0.475998i
$11$	0.403828	−	0.0921712i	0.121759	−	0.0277907i	−0.161207	−	0.986921i	$-0.551539\pi$
$11$	0.403828	−	0.0921712i	0.121759	−	0.0277907i	0.282966	+	0.959130i	$0.408682\pi$
$12$			9.24264i			2.66812i
$13$	−0.851905	−	3.73244i	−0.236276	−	1.03519i	−0.944321	−	0.329025i	$-0.893280\pi$
$13$	−0.851905	−	3.73244i	−0.236276	−	1.03519i	0.708045	−	0.706167i	$-0.249577\pi$
$14$	−2.96274	+	6.15220i	−0.791827	+	1.64424i
$15$	−1.04749	+	2.17513i	−0.270460	+	0.561616i
$16$	−0.667563	−	2.92478i	−0.166891	−	0.731196i
$17$		−	0.828427i		−	0.200923i	−0.994941	−	0.100462i	$-0.967968\pi$
$17$		−	0.828427i		−	0.200923i	0.994941	−	0.100462i	$-0.0320319\pi$
$18$	−6.65722	+	1.51947i	−1.56912	+	0.358142i
$19$	−4.69099	−	3.74094i	−1.07619	−	0.858230i	−0.0857663	−	0.996315i	$-0.527334\pi$
$19$	−4.69099	−	3.74094i	−1.07619	−	0.858230i	−0.990420	+	0.138085i	$0.955905\pi$
$20$	0.851905	−	3.73244i	0.190492	−	0.834599i
$21$	−6.65722	−	1.51947i	−1.45273	−	0.331575i
$22$	−0.623490	−	0.781831i	−0.132928	−	0.166687i
$23$	−3.29471	−	1.58665i	−0.686995	−	0.330839i	0.0576153	−	0.998339i	$-0.481650\pi$
$23$	−3.29471	−	1.58665i	−0.686995	−	0.330839i	−0.744610	+	0.667500i	$0.767365\pi$
$24$	9.60149	−	4.62384i	1.95990	−	0.943837i
$25$	−2.49396	+	3.12733i	−0.498792	+	0.625465i
$26$	−7.22619	+	5.76269i	−1.41717	+	1.13016i
$27$	0.179721	+	0.373194i	0.0345872	+	0.0718211i
$28$	10.8284			2.04638
$29$		0			0
$29$		0			0
$30$	5.82843			1.06412
$31$	4.36967	+	9.07372i	0.784816	+	1.62969i	0.776822	+	0.629720i	$0.216830\pi$
$31$	4.36967	+	9.07372i	0.784816	+	1.62969i	0.00799410	+	0.999968i	$0.497455\pi$
$32$	1.23982	−	0.988722i	0.219171	−	0.174783i
$33$	0.623490	−	0.781831i	0.108536	−	0.136099i
$34$	−1.80194	+	0.867767i	−0.309030	+	0.148821i
$35$	2.54832	+	1.22721i	0.430746	+	0.207436i
$36$	6.75141	+	8.46601i	1.12524	+	1.41100i
$37$	3.89971	+	0.890084i	0.641109	+	0.146329i	0.530703	−	0.847558i	$-0.321928\pi$
$37$	3.89971	+	0.890084i	0.641109	+	0.146329i	0.110405	+	0.993887i	$0.464785\pi$
$38$	−3.22328	+	14.1221i	−0.522885	+	2.29091i
$39$	−7.22619	−	5.76269i	−1.15712	−	0.922769i
$40$	−4.30354	+	0.982255i	−0.680449	+	0.155308i
$41$		−	4.48528i		−	0.700483i	−0.936659	−	0.350242i	$-0.886099\pi$
$41$		−	4.48528i		−	0.700483i	0.936659	−	0.350242i	$-0.113901\pi$
$42$	3.66832	+	16.0720i	0.566034	+	2.47996i
$43$	−1.55581	+	3.23068i	−0.237259	+	0.492674i	−0.985269	−	0.171014i	$-0.945296\pi$
$43$	−1.55581	+	3.23068i	−0.237259	+	0.492674i	0.748009	+	0.663688i	$0.231010\pi$
$44$	−0.688047	+	1.42874i	−0.103727	+	0.215391i
$45$	0.629384	+	2.75751i	0.0938231	+	0.411066i
$46$			8.82843i			1.30168i
$47$	−3.16134	+	0.721555i	−0.461129	+	0.105250i	−0.446773	−	0.894647i	$-0.647427\pi$
$47$	−3.16134	+	0.721555i	−0.461129	+	0.105250i	−0.0143558	+	0.999897i	$0.504570\pi$
$48$	−5.66252	−	4.51571i	−0.817315	−	0.651787i
$49$	−0.222521	+	0.974928i	−0.0317887	+	0.139275i
$50$	9.41474	+	2.14885i	1.33144	+	0.303894i
$51$	−1.24698	−	1.56366i	−0.174612	−	0.218957i
$52$	13.2054	+	6.35937i	1.83126	+	0.881886i
$53$	−8.54594	+	4.11551i	−1.17388	+	0.565309i	−0.916121	−	0.400902i	$-0.868697\pi$
$53$	−8.54594	+	4.11551i	−1.17388	+	0.565309i	−0.257755	+	0.966210i	$0.582983\pi$
$54$	0.623490	−	0.781831i	0.0848462	−	0.106394i
$55$	−0.323845	+	0.258258i	−0.0436673	+	0.0348235i
$56$	−5.41716	−	11.2488i	−0.723899	−	1.50319i
$57$	−14.4853			−1.91862
$58$		0			0
$59$	−3.65685			−0.476082			−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685			−0.476082			−0.238041	+	0.971255i	$0.576505\pi$
$60$	−4.01023	−	8.32733i	−0.517719	−	1.07505i
$61$	−3.77502	+	3.01048i	−0.483341	+	0.385452i	−0.834626	−	0.550817i	$-0.814316\pi$
$61$	−3.77502	+	3.01048i	−0.483341	+	0.385452i	0.351285	+	0.936269i	$0.385745\pi$
$62$	15.1593	−	19.0092i	1.92524	−	2.41417i
$63$	−7.20775	+	3.47107i	−0.908091	+	0.437314i
$64$	−8.85511	−	4.26439i	−1.10689	−	0.533049i
$65$	2.38699	+	2.99318i	0.296069	+	0.371259i
$66$	−2.35368	−	0.537213i	−0.289718	−	0.0661264i
$67$	1.25877	−	5.51503i	0.153783	−	0.673768i	−0.837982	−	0.545698i	$-0.816265\pi$
$67$	1.25877	−	5.51503i	0.153783	−	0.673768i	0.991765	−	0.128070i	$-0.0408782\pi$
$68$	2.47964	+	1.97744i	0.300700	+	0.239800i
$69$	−8.60708	+	1.96451i	−1.03617	+	0.236499i
$70$		−	6.82843i		−	0.816153i
$71$	−1.96451	−	8.60708i	−0.233144	−	1.02147i	−0.947014	−	0.321193i	$-0.895916\pi$
$71$	−1.96451	−	8.60708i	−0.233144	−	1.02147i	0.713869	−	0.700279i	$-0.246941\pi$
$72$	5.41716	−	11.2488i	0.638418	−	1.32569i
$73$	1.73553	−	3.60388i	0.203129	−	0.421802i	−0.774373	−	0.632730i	$-0.781934\pi$
$73$	1.73553	−	3.60388i	0.203129	−	0.421802i	0.977502	+	0.210928i	$0.0676486\pi$
$74$	−2.14885	−	9.41474i	−0.249799	−	1.09444i
$75$			9.65685i			1.11508i
$76$	22.3946	−	5.11143i	2.56884	−	0.586321i
$77$	−0.915973	−	0.730464i	−0.104385	−	0.0832441i
$78$	−4.96527	+	21.7543i	−0.562206	+	2.46318i
$79$	−2.35368	−	0.537213i	−0.264810	−	0.0604412i	0.0880542	−	0.996116i	$-0.471935\pi$
$79$	−2.35368	−	0.537213i	−0.264810	−	0.0604412i	−0.352864	+	0.935674i	$0.614792\pi$
$80$	1.87047	+	2.34549i	0.209125	+	0.262234i
$81$	8.54594	+	4.11551i	0.949549	+	0.457279i
$82$	−9.75608	+	4.69828i	−1.07738	+	0.518838i
$83$	4.77397	−	5.98637i	0.524011	−	0.657089i	−0.447444	−	0.894312i	$-0.647666\pi$
$83$	4.77397	−	5.98637i	0.524011	−	0.657089i	0.971455	+	0.237223i	$0.0762370\pi$
$84$	20.4387	−	16.2994i	2.23005	−	1.77841i
$85$	0.359441	+	0.746387i	0.0389869	+	0.0809570i
$86$	8.65685			0.933493
$87$		0			0
$88$	1.82843			0.194911
$89$	−5.41716	−	11.2488i	−0.574218	−	1.19238i	−0.962612	−	0.270883i	$-0.912685\pi$
$89$	−5.41716	−	11.2488i	−0.574218	−	1.19238i	0.388395	−	0.921493i	$-0.373030\pi$
$90$	5.33868	−	4.25745i	0.562746	−	0.448775i
$91$	−6.75141	+	8.46601i	−0.707740	+	0.887478i
$92$	12.6136	−	6.07437i	1.31505	−	0.633297i
$93$	21.9059	+	10.5493i	2.27154	+	1.09391i
$94$	4.88094	+	6.12051i	0.503431	+	0.631282i
$95$	5.84957	+	1.33513i	0.600153	+	0.136981i
$96$	0.851905	−	3.73244i	0.0869472	−	0.380941i
$97$	3.50673	+	2.79653i	0.356055	+	0.283944i	0.785138	−	0.619321i	$-0.212592\pi$
$97$	3.50673	+	2.79653i	0.356055	+	0.283944i	−0.429083	+	0.903265i	$0.641163\pi$
$98$	2.35368	−	0.537213i	0.237758	−	0.0542667i
$99$		−	1.17157i		−	0.117748i
$100$	−3.40762	−	14.9298i	−0.340762	−	1.49298i
$101$	1.01665	−	2.11110i	0.101161	−	0.210062i	−0.844246	−	0.535957i	$-0.819951\pi$
$101$	1.01665	−	2.11110i	0.101161	−	0.210062i	0.945406	+	0.325894i	$0.105665\pi$
$102$	−2.09498	+	4.35026i	−0.207434	+	0.430740i
$103$	1.07443	+	4.70737i	0.105866	+	0.463831i	0.999875	+	0.0157820i	$0.00502377\pi$
$103$	1.07443	+	4.70737i	0.105866	+	0.463831i	−0.894009	+	0.448049i	$0.852119\pi$
$104$		−	16.8995i		−	1.65713i
$105$	6.65722	−	1.51947i	0.649679	−	0.148285i
$106$	17.9035	+	14.2776i	1.73895	+	1.38676i
$107$	3.29964	−	14.4566i	0.318988	−	1.39758i	−0.520344	−	0.853957i	$-0.674196\pi$
$107$	3.29964	−	14.4566i	0.318988	−	1.39758i	0.839331	−	0.543620i	$-0.182947\pi$
$108$	−1.54603	−	0.352871i	−0.148767	−	0.0339550i
$109$	−7.89142	−	9.89553i	−0.755861	−	0.947820i	0.243897	−	0.969801i	$-0.421574\pi$
$109$	−7.89142	−	9.89553i	−0.755861	−	0.947820i	−0.999758	+	0.0219814i	$0.993003\pi$
$110$	0.900969	+	0.433884i	0.0859040	+	0.0413692i
$111$	8.70053	−	4.18995i	0.825817	−	0.397693i
$112$	−5.29049	+	6.63406i	−0.499904	+	0.626860i
$113$	10.4091	−	8.30096i	0.979204	−	0.780889i	0.00350228	−	0.999994i	$-0.498885\pi$
$113$	10.4091	−	8.30096i	0.979204	−	0.780889i	0.975701	+	0.219105i	$0.0703138\pi$
$114$	15.1732	+	31.5074i	1.42110	+	2.95094i
$115$	3.65685			0.341003
$116$		0			0
$117$	−10.8284			−1.00109
$118$	3.83051	+	7.95414i	0.352627	+	0.732238i
$119$	−1.83195	+	1.46093i	−0.167934	+	0.133923i
$120$	−6.64444	+	8.33186i	−0.606552	+	0.760592i
$121$	−9.75608	+	4.69828i	−0.886916	+	0.427116i
$122$	10.5025	+	5.05772i	0.950848	+	0.457904i
$123$	−6.75141	−	8.46601i	−0.608754	−	0.763354i
$124$	−37.5897	−	8.57959i	−3.37565	−	0.770470i
$125$	2.00269	−	8.77435i	0.179126	−	0.784802i
$126$	15.1001	+	12.0419i	1.34522	+	1.07278i
$127$	4.23425	−	0.966441i	0.375729	−	0.0857578i	−0.0304859	−	0.999535i	$-0.509705\pi$
$127$	4.23425	−	0.966441i	0.375729	−	0.0857578i	0.406215	+	0.913777i	$0.366848\pi$
$128$			20.5563i			1.81694i
$129$	1.92633	+	8.43981i	0.169604	+	0.743084i
$130$	4.01023	−	8.32733i	0.351721	−	0.730355i
$131$	9.24767	−	19.2030i	0.807973	−	1.67777i	0.0753308	−	0.997159i	$-0.475999\pi$
$131$	9.24767	−	19.2030i	0.807973	−	1.67777i	0.732642	−	0.680614i	$-0.238287\pi$
$132$	0.851905	+	3.73244i	0.0741488	+	0.324867i
$133$			16.9706i			1.47153i
$134$	−13.3144	+	3.03894i	−1.15019	+	0.262524i
$135$	−0.323845	−	0.258258i	−0.0278722	−	0.0222273i
$136$	0.813727	−	3.56517i	0.0697765	−	0.305711i
$137$	11.6991	+	2.67025i	0.999525	+	0.228135i	0.690823	−	0.723024i	$-0.257248\pi$
$137$	11.6991	+	2.67025i	0.999525	+	0.228135i	0.308702	+	0.951159i	$0.400106\pi$
$138$	13.2889	+	16.6637i	1.13122	+	1.41851i
$139$	−12.6136	−	6.07437i	−1.06987	−	0.515222i	−0.185804	−	0.982587i	$-0.559489\pi$
$139$	−12.6136	−	6.07437i	−1.06987	−	0.515222i	−0.884064	+	0.467365i	$0.845203\pi$
$140$	−9.75608	+	4.69828i	−0.824539	+	0.397077i
$141$	−4.88094	+	6.12051i	−0.411050	+	0.515440i
$142$	−16.6637	+	13.2889i	−1.39839	+	1.11518i
$143$	−0.688047	−	1.42874i	−0.0575374	−	0.119478i
$144$	−8.48528			−0.707107
$145$		0			0
$146$	−9.65685			−0.799207
$147$	1.04749	+	2.17513i	0.0863954	+	0.179402i
$148$	−11.9727	+	9.54794i	−0.984153	+	0.784836i
$149$	4.88094	−	6.12051i	0.399863	−	0.501412i	−0.540614	−	0.841271i	$-0.681808\pi$
$149$	4.88094	−	6.12051i	0.399863	−	0.501412i	0.940476	+	0.339859i	$0.110379\pi$
$150$	21.0049	−	10.1154i	1.71504	−	0.825922i
$151$	−12.7416	−	6.13604i	−1.03690	−	0.499344i	−0.163599	−	0.986527i	$-0.552310\pi$
$151$	−12.7416	−	6.13604i	−1.03690	−	0.499344i	−0.873300	+	0.487183i	$0.838025\pi$
$152$	−16.5133	−	20.7070i	−1.33941	−	1.67956i
$153$	−2.28440	−	0.521399i	−0.184683	−	0.0421526i
$154$	−0.629384	+	2.75751i	−0.0507172	+	0.222207i
$155$	−7.87388	−	6.27921i	−0.632445	−	0.504358i
$156$	34.4976	−	7.87385i	2.76202	−	0.630413i
$157$			8.48528i			0.677199i	0.940931	+	0.338600i	$0.109953\pi$
$157$			8.48528i			0.677199i	−0.940931	+	0.338600i	$0.890047\pi$
$158$	1.29695	+	5.68230i	0.103180	+	0.452059i
$159$	−9.93572	+	20.6317i	−0.787954	+	1.63620i
$160$	−0.688047	+	1.42874i	−0.0543949	+	0.112952i
$161$	2.30157	+	10.0838i	0.181389	+	0.794716i
$162$		−	22.8995i		−	1.79915i
$163$	3.83043	−	0.874270i	0.300022	−	0.0684781i	−0.0698599	−	0.997557i	$-0.522255\pi$
$163$	3.83043	−	0.874270i	0.300022	−	0.0684781i	0.369882	+	0.929079i	$0.379398\pi$
$164$	13.4253	+	10.7063i	1.04834	+	0.836022i
$165$	−0.222521	+	0.974928i	−0.0173232	+	0.0758980i
$166$	−18.0218	−	4.11336i	−1.39876	−	0.319259i
$167$	1.97744	+	2.47964i	0.153019	+	0.191880i	0.852432	−	0.522838i	$-0.175127\pi$
$167$	1.97744	+	2.47964i	0.153019	+	0.191880i	−0.699413	+	0.714718i	$0.746555\pi$
$168$	−27.1571	−	13.0782i	−2.09522	−	1.00900i
$169$	−1.49277	+	0.718882i	−0.114829	+	0.0552986i
$170$	1.24698	−	1.56366i	0.0956390	−	0.119927i
$171$	−13.2681	+	10.5810i	−1.01464	+	0.809147i
$172$	−5.95632	−	12.3684i	−0.454165	−	0.943084i
$173$	−12.3431			−0.938432			−0.469216	−	0.883083i	$-0.655463\pi$
$173$	−12.3431			−0.938432			−0.469216	+	0.883083i	$0.655463\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$	−0.539162	−	1.11958i	−0.0406408	−	0.0843916i
$177$	−6.90234	+	5.50443i	−0.518812	+	0.413739i
$178$	−18.7933	+	23.5661i	−1.40862	+	1.76635i
$179$	−5.84304	+	2.81386i	−0.436729	+	0.210318i	−0.639312	−	0.768947i	$-0.720781\pi$
$179$	−5.84304	+	2.81386i	−0.436729	+	0.210318i	0.202583	+	0.979265i	$0.435066\pi$
$180$	−9.75608	−	4.69828i	−0.727175	−	0.350189i
$181$	5.18351	+	6.49992i	0.385287	+	0.483135i	0.936220	−	0.351415i	$-0.114299\pi$
$181$	5.18351	+	6.49992i	0.385287	+	0.483135i	−0.550932	+	0.834550i	$0.685728\pi$
$182$	25.4867	+	5.81717i	1.88920	+	0.431198i
$183$	−2.59389	+	11.3646i	−0.191746	+	0.840095i
$184$	−12.6204	−	10.0645i	−0.930390	−	0.741962i
$185$	−3.89971	+	0.890084i	−0.286713	+	0.0654403i
$186$		−	58.6985i		−	4.30398i
$187$	−0.0763571	−	0.334542i	−0.00558379	−	0.0244642i
$188$	5.38633	−	11.1848i	0.392838	−	0.815737i
$189$	0.508326	−	1.05555i	0.0369753	−	0.0767800i
$190$	−3.22328	−	14.1221i	−0.233841	−	1.02453i
$191$		−	25.3137i		−	1.83164i	−0.401594	−	0.915818i	$-0.631544\pi$
$191$		−	25.3137i		−	1.83164i	0.401594	−	0.915818i	$-0.368456\pi$
$192$	−23.1330	+	5.27996i	−1.66948	+	0.381048i
$193$	4.04330	+	3.22442i	0.291043	+	0.232099i	0.758116	−	0.652120i	$-0.226120\pi$
$193$	4.04330	+	3.22442i	0.291043	+	0.232099i	−0.467073	+	0.884219i	$0.654691\pi$
$194$	2.40955	−	10.5569i	0.172996	−	0.757944i
$195$	9.01091	+	2.05668i	0.645285	+	0.147282i
$196$	−2.38699	−	2.99318i	−0.170499	−	0.213799i
$197$	−1.80194	−	0.867767i	−0.128383	−	0.0618259i	0.368590	−	0.929592i	$-0.379841\pi$
$197$	−1.80194	−	0.867767i	−0.128383	−	0.0618259i	−0.496972	+	0.867766i	$0.665555\pi$
$198$	−2.54832	+	1.22721i	−0.181102	+	0.0872139i
$199$	−0.302568	+	0.379408i	−0.0214485	+	0.0268955i	−0.792440	−	0.609950i	$-0.791190\pi$
$199$	−0.302568	+	0.379408i	−0.0214485	+	0.0268955i	0.770992	+	0.636845i	$0.219761\pi$
$200$	−13.8047	+	11.0089i	−0.976139	+	0.778445i
$201$	−5.92549	−	12.3044i	−0.417952	−	0.867885i
$202$	−5.65685			−0.398015
$203$		0			0
$204$	7.65685			0.536087
$205$	1.94609	+	4.04110i	0.135921	+	0.282243i
$206$	9.11370	−	7.26793i	0.634981	−	0.506381i
$207$	−6.44885	+	8.08660i	−0.448226	+	0.562057i
$208$	−10.3479	+	4.98328i	−0.717496	+	0.345528i
$209$	−2.23916	−	1.07832i	−0.154886	−	0.0745892i
$210$	−10.2784	−	12.8887i	−0.709277	−	0.889406i
$211$	18.8988	+	4.31352i	1.30104	+	0.296955i	0.816263	−	0.577681i	$-0.196042\pi$
$211$	18.8988	+	4.31352i	1.30104	+	0.296955i	0.484781	+	0.874635i	$0.338899\pi$
$212$	8.08056	−	35.4032i	0.554975	−	2.43151i
$213$	−16.6637	−	13.2889i	−1.14178	−	0.910539i
$214$	−34.9014	+	7.96602i	−2.38581	+	0.544546i
$215$		−	3.58579i		−	0.244549i
$216$	0.406863	+	1.78258i	0.0276835	+	0.121290i
$217$	12.3593	−	25.6644i	0.839004	−	1.74221i
$218$	−13.2579	+	27.5303i	−0.897938	+	1.86459i
$219$	−2.14885	−	9.41474i	−0.145206	−	0.636189i
$220$		−	1.58579i		−	0.106914i
$221$	−3.09205	+	0.705741i	−0.207994	+	0.0474733i
$222$	−18.2274	−	14.5359i	−1.22334	−	0.975583i
$223$	0.705741	−	3.09205i	0.0472599	−	0.207059i	−0.945785	−	0.324792i	$-0.894706\pi$
$223$	0.705741	−	3.09205i	0.0472599	−	0.207059i	0.993045	+	0.117733i	$0.0375627\pi$
$224$	−4.37283	−	0.998069i	−0.292172	−	0.0666863i
$225$	7.05398	+	8.84541i	0.470265	+	0.589694i
$226$	−28.9591	−	13.9459i	−1.92633	−	0.927671i
$227$	7.33581	−	3.53274i	0.486895	−	0.234476i	−0.174297	−	0.984693i	$-0.555765\pi$
$227$	7.33581	−	3.53274i	0.486895	−	0.234476i	0.661192	+	0.750217i	$0.270051\pi$
$228$	34.5762	−	43.3571i	2.28986	−	2.87140i
$229$	2.74792	−	2.19139i	0.181588	−	0.144811i	−0.528478	−	0.848947i	$-0.677237\pi$
$229$	2.74792	−	2.19139i	0.181588	−	0.144811i	0.710065	+	0.704136i	$0.248666\pi$
$230$	−3.83051	−	7.95414i	−0.252576	−	0.524480i
$231$	−2.82843			−0.186097
$232$		0			0
$233$	18.3137			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$234$	11.3426	+	23.5533i	0.741492	+	1.53972i
$235$	2.53520	−	2.02175i	0.165378	−	0.131885i
$236$	8.72886	−	10.9456i	0.568200	−	0.712501i
$237$	−5.25123	+	2.52886i	−0.341104	+	0.164267i
$238$	5.09665	+	2.45442i	0.330367	+	0.159096i
$239$	−12.2558	−	15.3683i	−0.792765	−	0.994096i	−0.999876	−	0.0157782i	$-0.994977\pi$
$239$	−12.2558	−	15.3683i	−0.792765	−	0.994096i	0.207111	−	0.978318i	$-0.433594\pi$
$240$	7.06105	+	1.61164i	0.455789	+	0.104031i
$241$	−4.07518	+	17.8545i	−0.262506	+	1.15011i	0.656018	+	0.754746i	$0.272240\pi$
$241$	−4.07518	+	17.8545i	−0.262506	+	1.15011i	−0.918523	+	0.395367i	$0.870617\pi$
$242$	20.4387	+	16.2994i	1.31385	+	1.04776i
$243$	21.1139	−	4.81910i	1.35446	−	0.309146i
$244$		−	18.4853i		−	1.18340i
$245$	−0.222521	−	0.974928i	−0.0142163	−	0.0622859i
$246$	−11.3426	+	23.5533i	−0.723181	+	1.50170i
$247$	−9.96655	+	20.6958i	−0.634157	+	1.31684i
$248$	9.89236	+	43.3412i	0.628165	+	2.75217i
$249$		−	18.4853i		−	1.17146i
$250$	−21.1832	+	4.83492i	−1.33974	+	0.305787i
$251$	−15.6922	−	12.5141i	−0.990482	−	0.789883i	−0.0127885	−	0.999918i	$-0.504071\pi$
$251$	−15.6922	−	12.5141i	−0.990482	−	0.789883i	−0.977694	+	0.210035i	$0.932642\pi$
$252$	6.81524	−	29.8595i	0.429320	−	1.88097i
$253$	−1.47674	−	0.337057i	−0.0928419	−	0.0211906i
$254$	−6.53747	−	8.19772i	−0.410197	−	0.514371i
$255$	1.80194	+	0.867767i	0.112842	+	0.0543417i
$256$	27.0025	−	13.0037i	1.68766	−	0.812734i
$257$	−11.3298	+	14.2071i	−0.706733	+	0.886215i	−0.997506	−	0.0705769i	$-0.977516\pi$
$257$	−11.3298	+	14.2071i	−0.706733	+	0.886215i	0.290773	+	0.956792i	$0.406087\pi$
$258$	16.3399	−	13.0306i	1.01728	−	0.811251i
$259$	−4.90883	−	10.1933i	−0.305020	−	0.633381i
$260$	−14.6569			−0.908980
$261$		0			0
$262$	−51.4558			−3.17895
$263$	1.19637	+	2.48429i	0.0737715	+	0.153188i	0.934593	−	0.355719i	$-0.115764\pi$
$263$	1.19637	+	2.48429i	0.0737715	+	0.153188i	−0.860821	+	0.508907i	$0.830050\pi$
$264$	3.45117	−	2.75222i	0.212405	−	0.169387i
$265$	5.91398	−	7.41589i	0.363293	−	0.455555i
$266$	36.9132	−	17.7765i	2.26329	−	1.08994i
$267$	−27.1571	−	13.0782i	−1.66199	−	0.800372i
$268$	13.5028	+	16.9320i	0.824816	+	1.03429i
$269$	−30.6672	−	6.99958i	−1.86981	−	0.426772i	−0.871803	−	0.489857i	$-0.837049\pi$
$269$	−30.6672	−	6.99958i	−1.86981	−	0.426772i	−0.998008	+	0.0630848i	$0.979906\pi$
$270$	−0.222521	+	0.974928i	−0.0135422	+	0.0593322i
$271$	12.9443	+	10.3227i	0.786309	+	0.627060i	0.932078	−	0.362258i	$-0.117994\pi$
$271$	12.9443	+	10.3227i	0.786309	+	0.627060i	−0.145769	+	0.989319i	$0.546566\pi$
$272$	−2.42297	+	0.553027i	−0.146914	+	0.0335322i
$273$			26.1421i			1.58219i
$274$	−6.44656	−	28.2442i	−0.389451	−	1.70630i
$275$	−0.718882	+	1.49277i	−0.0433502	+	0.0900177i
$276$	14.6648	−	30.4518i	0.882719	−	1.83299i
$277$	3.85266	+	16.8796i	0.231484	+	1.01420i	0.948409	+	0.317048i	$0.102692\pi$
$277$	3.85266	+	16.8796i	0.231484	+	1.01420i	−0.716925	+	0.697150i	$0.754451\pi$
$278$			33.7990i			2.02713i
$279$	27.7711	−	6.33857i	1.66261	−	0.379480i
$280$	9.76139	+	7.78445i	0.583354	+	0.465210i
$281$	−7.11412	+	31.1690i	−0.424393	+	1.85939i	0.0813255	+	0.996688i	$0.474085\pi$
$281$	−7.11412	+	31.1690i	−0.424393	+	1.85939i	−0.505718	+	0.862699i	$0.668772\pi$
$282$	18.4256	+	4.20553i	1.09723	+	0.250436i
$283$	−7.26793	−	9.11370i	−0.432034	−	0.541753i	0.517391	−	0.855749i	$-0.326903\pi$
$283$	−7.26793	−	9.11370i	−0.432034	−	0.541753i	−0.949424	+	0.313996i	$0.898332\pi$
$284$	30.4518	+	14.6648i	1.80698	+	0.870198i
$285$	13.0508	−	6.28493i	0.773062	−	0.372287i
$286$	−2.38699	+	2.99318i	−0.141145	+	0.176991i
$287$	−9.91854	+	7.90977i	−0.585473	+	0.466899i
$288$	−1.94609	−	4.04110i	−0.114674	−	0.238124i
$289$	16.3137			0.959630
$290$		0			0
$291$	10.8284			0.634774
$292$	6.64437	+	13.7972i	0.388832	+	0.807419i
$293$	5.98637	−	4.77397i	0.349727	−	0.278898i	−0.432831	−	0.901475i	$-0.642485\pi$
$293$	5.98637	−	4.77397i	0.349727	−	0.278898i	0.782559	+	0.622577i	$0.213914\pi$
$294$	3.63396	−	4.55685i	0.211937	−	0.265761i
$295$	3.29471	−	1.58665i	0.191826	−	0.0923783i
$296$	15.9083	+	7.66102i	0.924650	+	0.445288i
$297$	0.106974	+	0.134141i	0.00620726	+	0.00778365i
$298$	−18.4256	−	4.20553i	−1.06737	−	0.243620i
$299$	−3.11529	+	13.6490i	−0.180162	+	0.789342i
$300$	−28.9047	−	23.0508i	−1.66882	−	1.33084i
$301$	9.88785	−	2.25684i	0.569926	−	0.130082i
$302$			34.1421i			1.96466i
$303$	−1.25877	−	5.51503i	−0.0723144	−	0.316830i
$304$	−7.80991	+	16.2174i	−0.447929	+	0.930134i
$305$	2.09498	−	4.35026i	0.119958	−	0.249095i
$306$	1.25877	+	5.51503i	0.0719590	+	0.315273i
$307$		−	2.89949i		−	0.165483i	−0.996571	−	0.0827415i	$-0.973632\pi$
$307$		−	2.89949i		−	0.165483i	0.996571	−	0.0827415i	$-0.0263676\pi$
$308$	4.37283	−	0.998069i	0.249165	−	0.0568703i
$309$	9.11370	+	7.26793i	0.518460	+	0.413458i
$310$	−5.41031	+	23.7041i	−0.307285	+	1.34630i
$311$	2.61894	+	0.597756i	0.148506	+	0.0338956i	0.296128	−	0.955148i	$-0.404305\pi$
$311$	2.61894	+	0.597756i	0.148506	+	0.0338956i	−0.147621	+	0.989044i	$0.547162\pi$
$312$	−25.4378	−	31.8979i	−1.44013	−	1.80586i
$313$	−8.85511	−	4.26439i	−0.500520	−	0.241038i	0.166550	−	0.986033i	$-0.446737\pi$
$313$	−8.85511	−	4.26439i	−0.500520	−	0.241038i	−0.667070	+	0.744995i	$0.732452\pi$
$314$	18.4566	−	8.88823i	1.04157	−	0.501592i
$315$	4.98792	−	6.25465i	0.281037	−	0.352410i
$316$	7.22619	−	5.76269i	0.406505	−	0.324177i
$317$	13.6482	+	28.3407i	0.766558	+	1.59177i	0.805545	+	0.592535i	$0.201873\pi$
$317$	13.6482	+	28.3407i	0.766558	+	1.59177i	−0.0389869	+	0.999240i	$0.512413\pi$
$318$	55.2843			3.10019
$319$		0			0
$320$	9.82843			0.549426
$321$	−15.5326	−	32.2538i	−0.866945	−	1.80023i
$322$	19.5228	−	15.5689i	1.08796	−	0.867620i
$323$	−3.09910	+	3.88614i	−0.172438	+	0.216231i
$324$	−32.7175	+	15.7559i	−1.81764	+	0.875329i
$325$	13.7972	+	6.64437i	0.765330	+	0.368563i
$326$	−5.91398	−	7.41589i	−0.327545	−	0.410728i
$327$	−29.7902	−	6.79943i	−1.64740	−	0.376009i
$328$	4.40569	−	19.3026i	0.243264	−	1.06581i
$329$	7.17062	+	5.71838i	0.395329	+	0.315265i
$330$	2.35368	−	0.537213i	0.129566	−	0.0295726i
$331$		−	2.41421i		−	0.132697i	−0.997797	−	0.0663486i	$-0.978865\pi$
$331$		−	2.41421i		−	0.132697i	0.997797	−	0.0663486i	$-0.0211349\pi$
$332$	6.52291	+	28.5788i	0.357991	+	1.56846i
$333$	4.90883	−	10.1933i	0.269002	−	0.558589i
$334$	3.32218	−	6.89859i	0.181782	−	0.377474i
$335$	1.25877	+	5.51503i	0.0687739	+	0.301318i
$336$			20.4853i			1.11756i
$337$	21.2524	−	4.85073i	1.15769	−	0.264236i	0.399793	−	0.916605i	$-0.369082\pi$
$337$	21.2524	−	4.85073i	1.15769	−	0.264236i	0.757901	+	0.652369i	$0.226225\pi$
$338$	3.12733	+	2.49396i	0.170104	+	0.135653i
$339$	7.15230	−	31.3363i	0.388460	−	1.70195i
$340$	−3.09205	−	0.705741i	−0.167690	−	0.0382742i
$341$	2.60093	+	3.26147i	0.140848	+	0.176618i
$342$	36.9132	+	17.7765i	1.99604	+	0.961241i
$343$	−15.2899	+	7.36325i	−0.825580	+	0.397578i
$344$	−9.86886	+	12.3752i	−0.532093	+	0.667224i
$345$	6.90234	−	5.50443i	0.371610	−	0.296349i
$346$	12.9293	+	26.8480i	0.695083	+	1.44336i
$347$	−2.48528			−0.133417			−0.0667084	−	0.997773i	$-0.521250\pi$
$347$	−2.48528			−0.133417			−0.0667084	+	0.997773i	$0.521250\pi$
$348$		0			0
$349$	−5.14214			−0.275252			−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214			−0.275252			−0.137626	+	0.990484i	$0.543947\pi$
$350$	−11.8510	−	24.6088i	−0.633461	−	1.31540i
$351$	1.23982	−	0.988722i	0.0661766	−	0.0527741i
$352$	0.409542	−	0.513549i	0.0218287	−	0.0273723i
$353$	24.2996	−	11.7021i	1.29334	−	0.622839i	0.344556	−	0.938766i	$-0.388030\pi$
$353$	24.2996	−	11.7021i	1.29334	−	0.622839i	0.948784	+	0.315927i	$0.102315\pi$
$354$	19.2030	+	9.24767i	1.02063	+	0.491508i
$355$	5.50443	+	6.90234i	0.292145	+	0.366338i
$356$	46.6006	+	10.6363i	2.46983	+	0.563721i
$357$	−1.25877	+	5.51503i	−0.0666211	+	0.291886i
$358$	12.2410	+	9.76189i	0.646958	+	0.515932i
$359$	−3.83043	+	0.874270i	−0.202162	+	0.0461422i	−0.322403	−	0.946603i	$-0.604491\pi$
$359$	−3.83043	+	0.874270i	−0.202162	+	0.0461422i	0.120241	+	0.992745i	$0.461633\pi$
$360$			12.4853i			0.658032i
$361$	3.78286	+	16.5738i	0.199098	+	0.872304i
$362$	8.70851	−	18.0834i	0.457709	−	0.950443i
$363$	−11.3426	+	23.5533i	−0.595335	+	1.23623i
$364$	−9.22479	−	40.4165i	−0.483511	−	2.11840i
$365$			4.00000i			0.209370i
$366$	27.4366	−	6.26221i	1.43413	−	0.327331i
$367$	−14.0730	−	11.2228i	−0.734603	−	0.585826i	0.183100	−	0.983094i	$-0.441387\pi$
$367$	−14.0730	−	11.2228i	−0.734603	−	0.585826i	−0.917703	+	0.397268i	$0.869958\pi$
$368$	−2.44118	+	10.6955i	−0.127255	+	0.557542i
$369$	−12.3682	−	2.82297i	−0.643864	−	0.146958i
$370$	6.02095	+	7.55003i	0.313014	+	0.392508i
$371$	24.1716	+	11.6404i	1.25493	+	0.604340i
$372$	−83.8651	+	40.3873i	−4.34820	+	2.09398i
$373$	−16.4063	+	20.5729i	−0.849488	+	1.06522i	0.147607	+	0.989046i	$0.452843\pi$
$373$	−16.4063	+	20.5729i	−0.849488	+	1.06522i	−0.997094	+	0.0761775i	$0.975728\pi$
$374$	−0.647690	+	0.516516i	−0.0334913	+	0.0267084i
$375$	−9.42739	−	19.5762i	−0.486828	−	1.01091i
$376$	−14.3137			−0.738173
$377$		0			0
$378$	−2.82843			−0.145479
$379$	−3.02441	−	6.28026i	−0.155354	−	0.322595i	0.808736	−	0.588172i	$-0.200152\pi$
$379$	−3.02441	−	6.28026i	−0.155354	−	0.322595i	−0.964090	+	0.265576i	$0.914438\pi$
$380$	−17.9591	+	14.3219i	−0.921283	+	0.734699i
$381$	6.53747	−	8.19772i	0.334925	−	0.419982i
$382$	−55.0606	+	26.5158i	−2.81715	+	1.35667i
$383$	−3.16665	−	1.52498i	−0.161808	−	0.0779228i	0.351227	−	0.936290i	$-0.385765\pi$
$383$	−3.16665	−	1.52498i	−0.161808	−	0.0779228i	−0.513035	+	0.858368i	$0.671479\pi$
$384$	30.9422	+	38.8003i	1.57901	+	1.98002i
$385$	1.14220	+	0.260699i	0.0582119	+	0.0132865i
$386$	2.77824	−	12.1722i	0.141409	−	0.619551i
$387$	7.92944	+	6.32352i	0.403076	+	0.321442i
$388$	−16.7410	+	3.82103i	−0.849898	+	0.193984i
$389$			3.02944i			0.153599i	0.997047	+	0.0767993i	$0.0244701\pi$
$389$			3.02944i			0.153599i	−0.997047	+	0.0767993i	$0.975530\pi$
$390$	−4.96527	−	21.7543i	−0.251426	−	1.10157i
$391$	−1.31442	+	2.72943i	−0.0664733	+	0.138033i
$392$	−1.91526	+	3.97707i	−0.0967350	+	0.200872i
$393$	−11.4500	−	50.1657i	−0.577576	−	2.53053i
$394$			4.82843i			0.243253i
$395$	2.35368	−	0.537213i	0.118427	−	0.0270301i
$396$	3.50673	+	2.79653i	0.176220	+	0.140531i
$397$	−4.30425	+	18.8582i	−0.216024	+	0.946465i	0.744358	+	0.667780i	$0.232755\pi$
$397$	−4.30425	+	18.8582i	−0.216024	+	0.946465i	−0.960383	+	0.278684i	$0.910102\pi$
$398$	1.14220	+	0.260699i	0.0572533	+	0.0130677i
$399$	25.5447	+	32.0321i	1.27884	+	1.60361i
$400$	10.8116	+	5.20660i	0.540581	+	0.260330i
$401$	16.8092	−	8.09491i	0.839414	−	0.404240i	0.0357764	−	0.999360i	$-0.488610\pi$
$401$	16.8092	−	8.09491i	0.839414	−	0.404240i	0.803637	+	0.595120i	$0.202895\pi$
$402$	−20.5568	+	25.7774i	−1.02528	+	1.28566i
$403$	30.1446	−	24.0395i	1.50161	−	1.19749i
$404$	3.89218	+	8.08220i	0.193643	+	0.402104i
$405$	−9.48528			−0.471327
$406$		0			0
$407$	1.65685			0.0821272
$408$	−3.83051	−	7.95414i	−0.189639	−	0.393789i
$409$	−14.8318	+	11.8280i	−0.733384	+	0.584855i	−0.917352	−	0.398078i	$-0.869677\pi$
$409$	−14.8318	+	11.8280i	−0.733384	+	0.584855i	0.183967	+	0.982932i	$0.441106\pi$
$410$	6.75141	−	8.46601i	0.333429	−	0.418106i
$411$	26.1016	−	12.5699i	1.28750	−	0.620025i
$412$	−16.6547	−	8.02046i	−0.820516	−	0.395140i
$413$	6.44885	+	8.08660i	0.317327	+	0.397915i
$414$	24.3445	+	5.55647i	1.19647	+	0.273086i
$415$	−1.70381	+	7.46488i	−0.0836368	+	0.366437i
$416$	−4.74655	−	3.78525i	−0.232719	−	0.185587i
$417$	−32.9516	+	7.52098i	−1.61365	+	0.368304i
$418$			6.00000i			0.293470i
$419$	−2.11722	−	9.27616i	−0.103433	−	0.453170i	−0.999948	−	0.0101574i	$-0.996767\pi$
$419$	−2.11722	−	9.27616i	−0.103433	−	0.453170i	0.896515	−	0.443013i	$-0.146090\pi$
$420$	−11.3426	+	23.5533i	−0.553465	+	1.14928i
$421$	16.1026	−	33.4374i	0.784793	−	1.62964i	0.00792973	−	0.999969i	$-0.497476\pi$
$421$	16.1026	−	33.4374i	0.784793	−	1.62964i	0.776863	−	0.629670i	$-0.216810\pi$
$422$	−10.4138	−	45.6256i	−0.506934	−	2.22102i
$423$			9.17157i			0.445937i
$424$	−40.8203	+	9.31696i	−1.98241	+	0.452472i
$425$	2.59076	+	2.06606i	0.125670	+	0.100219i
$426$	−11.4500	+	50.1657i	−0.554754	+	2.43054i
$427$	13.3144	+	3.03894i	0.644331	+	0.147064i
$428$	35.3952	+	44.3842i	1.71089	+	2.14539i
$429$	−3.44929	−	1.66109i	−0.166533	−	0.0801983i
$430$	−7.79956	+	3.75607i	−0.376128	+	0.181134i
$431$	12.2558	−	15.3683i	0.590343	−	0.740267i	−0.393495	−	0.919327i	$-0.628734\pi$
$431$	12.2558	−	15.3683i	0.590343	−	0.740267i	0.983838	+	0.179060i	$0.0573055\pi$
$432$	0.971536	−	0.774774i	0.0467430	−	0.0372763i
$433$	−13.2887	−	27.5943i	−0.638616	−	1.32610i	−0.929316	−	0.369286i	$-0.879602\pi$
$433$	−13.2887	−	27.5943i	−0.638616	−	1.32610i	0.290700	−	0.956814i	$-0.406112\pi$
$434$	−68.7696			−3.30104
$435$		0			0
$436$	48.4558			2.32061
$437$	9.51990	+	19.7683i	0.455398	+	0.945645i
$438$	−18.2274	+	14.5359i	−0.870938	+	0.694550i
$439$	0.213948	−	0.268282i	0.0102112	−	0.0128044i	−0.776700	−	0.629871i	$-0.783108\pi$
$439$	0.213948	−	0.268282i	0.0102112	−	0.0128044i	0.786911	+	0.617067i	$0.211679\pi$
$440$	−1.64736	+	0.793325i	−0.0785346	+	0.0378203i
$441$	2.54832	+	1.22721i	0.121349	+	0.0584385i
$442$	4.77397	+	5.98637i	0.227075	+	0.284743i
$443$	23.7328	+	5.41686i	1.12758	+	0.257363i	0.745330	−	0.666696i	$-0.232292\pi$
$443$	23.7328	+	5.41686i	1.12758	+	0.257363i	0.382250	+	0.924059i	$0.375149\pi$
$444$	−8.22672	+	36.0436i	−0.390423	+	1.71056i
$445$	9.76139	+	7.78445i	0.462734	+	0.369018i
$446$	−7.46488	+	1.70381i	−0.353472	+	0.0806778i
$447$		−	18.8995i		−	0.893915i
$448$	6.18586	+	27.1020i	0.292254	+	1.28045i
$449$	15.1732	−	31.5074i	0.716066	−	1.48693i	−0.150895	−	0.988550i	$-0.548216\pi$
$449$	15.1732	−	31.5074i	0.716066	−	1.48693i	0.866961	−	0.498376i	$-0.166070\pi$
$450$	11.8510	−	24.6088i	0.558660	−	1.16007i
$451$	−0.413414	−	1.81128i	−0.0194669	−	0.0852900i
$452$			50.9706i			2.39745i
$453$	−33.2861	+	7.59734i	−1.56392	+	0.356954i
$454$	−15.3683	−	12.2558i	−0.721272	−	0.575195i
$455$	2.40955	−	10.5569i	0.112962	−	0.494917i
$456$	−62.3380	−	14.2282i	−2.91924	−	0.666298i
$457$	−0.641844	−	0.804846i	−0.0300242	−	0.0376491i	0.766593	−	0.642134i	$-0.221951\pi$
$457$	−0.641844	−	0.804846i	−0.0300242	−	0.0376491i	−0.796617	+	0.604484i	$0.793379\pi$
$458$	−7.64497	−	3.68163i	−0.357226	−	0.172031i
$459$	0.309164	−	0.148885i	0.0144305	−	0.00694937i
$460$	−8.72886	+	10.9456i	−0.406985	+	0.510343i
$461$	−10.9456	+	8.72886i	−0.509789	+	0.406543i	−0.844318	−	0.535842i	$-0.819994\pi$
$461$	−10.9456	+	8.72886i	−0.509789	+	0.406543i	0.334529	+	0.942385i	$0.391423\pi$
$462$	2.96274	+	6.15220i	0.137839	+	0.286226i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$		0			0
$465$	−24.3137			−1.12752
$466$	−19.1834	−	39.8347i	−0.888653	−	1.84531i
$467$	−29.9874	+	23.9142i	−1.38765	+	1.10662i	−0.406441	+	0.913677i	$0.633230\pi$
$467$	−29.9874	+	23.9142i	−1.38765	+	1.10662i	−0.981211	+	0.192938i	$0.938198\pi$
$468$	25.8473	−	32.4115i	1.19479	−	1.49822i
$469$	−14.4155	+	6.94214i	−0.665646	+	0.320558i
$470$	−7.05317	−	3.39663i	−0.325338	−	0.156675i
$471$	12.7724	+	16.0160i	0.588519	+	0.737980i
$472$	−15.7374	−	3.59196i	−0.724373	−	0.165334i
$473$	−0.330506	+	1.44804i	−0.0151967	+	0.0665811i
$474$	11.0012	+	8.77317i	0.505302	+	0.402965i
$475$	23.3983	−	5.34050i	1.07359	−	0.245039i
$476$		−	8.97056i		−	0.411165i
$477$	5.96989	+	26.1558i	0.273342	+	1.19759i
$478$	−20.5903	+	42.7562i	−0.941779	+	1.95562i
$479$	2.99358	−	6.21623i	0.136780	−	0.284027i	−0.821316	−	0.570473i	$-0.806760\pi$
$479$	2.99358	−	6.21623i	0.136780	−	0.284027i	0.958096	+	0.286447i	$0.0924741\pi$
$480$	0.851905	+	3.73244i	0.0388840	+	0.170362i
$481$		−	15.3137i		−	0.698245i
$482$	43.1047	−	9.83836i	1.96336	−	0.448125i
$483$	19.5228	+	15.5689i	0.888317	+	0.708409i
$484$	9.22479	−	40.4165i	0.419309	−	1.83711i
$485$	−4.37283	−	0.998069i	−0.198560	−	0.0453200i
$486$	−32.5987	−	40.8775i	−1.47871	−	1.85424i
$487$	10.3744	+	4.99605i	0.470109	+	0.226393i	0.653912	−	0.756570i	$-0.273127\pi$
$487$	10.3744	+	4.99605i	0.470109	+	0.226393i	−0.183803	+	0.982963i	$0.558841\pi$
$488$	−19.2030	+	9.24767i	−0.869278	+	0.418622i
$489$	5.91398	−	7.41589i	0.267439	−	0.335358i
$490$	−1.88751	+	1.50524i	−0.0852689	+	0.0679997i
$491$	9.21684	+	19.1390i	0.415950	+	0.863729i	0.998695	+	0.0510739i	$0.0162644\pi$
$491$	9.21684	+	19.1390i	0.415950	+	0.863729i	−0.582745	+	0.812655i	$0.698021\pi$
$492$	41.4558			1.86897
$493$		0			0
$494$	55.4558			2.49508
$495$	0.508326	+	1.05555i	0.0228476	+	0.0474435i
$496$	23.6216	−	18.8376i	1.06064	−	0.845834i
$497$	−15.5689	+	19.5228i	−0.698360	+	0.875716i
$498$	−40.2079	+	19.3631i	−1.80176	+	0.867682i
$499$	17.0919	+	8.23102i	0.765138	+	0.368471i	0.775395	−	0.631476i	$-0.217551\pi$
$499$	17.0919	+	8.23102i	0.765138	+	0.368471i	−0.0102572	+	0.999947i	$0.503265\pi$
$500$	21.4829	+	26.9387i	0.960743	+	1.20473i
$501$	7.46488	+	1.70381i	0.333506	+	0.0761206i
$502$	−10.7824	+	47.2410i	−0.481244	+	2.10847i
$503$	0.212719	+	0.169638i	0.00948468	+	0.00756378i	0.628221	−	0.778035i	$-0.283784\pi$
$503$	0.212719	+	0.169638i	0.00948468	+	0.00756378i	−0.618736	+	0.785599i	$0.712355\pi$
$504$	−34.4283	+	7.85804i	−1.53356	+	0.350025i
$505$			2.34315i			0.104269i
$506$	0.813727	+	3.56517i	0.0361746	+	0.158491i
$507$	−1.73553	+	3.60388i	−0.0770778	+	0.160054i
$508$	−7.21437	+	14.9808i	−0.320086	+	0.664665i
$509$	2.33975	+	10.2511i	0.103707	+	0.454372i	0.999942	+	0.0107909i	$0.00343493\pi$
$509$	2.33975	+	10.2511i	0.103707	+	0.454372i	−0.896234	+	0.443581i	$0.853708\pi$
$510$		−	4.82843i		−	0.213806i
$511$	−11.0301	+	2.51754i	−0.487941	+	0.111369i
$512$	−24.4265	−	19.4795i	−1.07951	−	0.860879i
$513$	0.553027	−	2.42297i	0.0244167	−	0.106977i
$514$	42.7701	+	9.76201i	1.88651	+	0.430584i
$515$	−3.01048	−	3.77502i	−0.132657	−	0.166347i
$516$	−29.8600	−	14.3798i	−1.31451	−	0.633037i
$517$	−1.21013	+	0.582769i	−0.0532216	+	0.0256302i
$518$	−17.0298	+	21.3547i	−0.748247	+	0.938272i
$519$	−23.2978	+	18.5794i	−1.02266	+	0.815544i
$520$	7.33242	+	15.2259i	0.321548	+	0.667701i
$521$	29.1421			1.27674			0.638370	−	0.769730i	$-0.279609\pi$
$521$	29.1421			1.27674			0.638370	+	0.769730i	$0.279609\pi$
$522$		0			0
$523$	4.68629			0.204917			0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629			0.204917			0.102459	+	0.994737i	$0.467329\pi$
$524$	35.4040	+	73.5172i	1.54663	+	3.21162i
$525$	21.3547	−	17.0298i	0.931996	−	0.743242i
$526$	4.15048	−	5.20454i	0.180970	−	0.226929i
$527$	7.51691	−	3.61996i	0.327442	−	0.157688i
$528$	−2.70291	−	1.30165i	−0.117629	−	0.0566471i
$529$	−6.00260	−	7.52702i	−0.260982	−	0.327262i
$530$	−22.3254	−	5.09562i	−0.969752	−	0.221339i
$531$	−2.30157	+	10.0838i	−0.0998795	+	0.437601i
$532$	−50.7960	−	40.5085i	−2.20229	−	1.75627i
$533$	−16.7410	+	3.82103i	−0.725135	+	0.165507i
$534$			72.7696i			3.14905i
$535$	3.29964	+	14.4566i	0.142656	+	0.625015i
$536$	10.8343	−	22.4977i	0.467971	−	0.971753i
$537$	−6.79325	+	14.1063i	−0.293151	+	0.608733i
$538$	16.8985	+	74.0371i	0.728546	+	3.19197i
$539$			0.414214i			0.0178414i
$540$	1.54603	−	0.352871i	0.0665304	−	0.0151851i
$541$	8.08660	+	6.44885i	0.347670	+	0.277258i	0.781718	−	0.623632i	$-0.214344\pi$
$541$	8.08660	+	6.44885i	0.347670	+	0.277258i	−0.434048	+	0.900890i	$0.642915\pi$
$542$	8.89429	−	38.9684i	0.382042	−	1.67384i
$543$	19.5678	+	4.46623i	0.839737	+	0.191664i
$544$	−0.819084	−	1.02710i	−0.0351179	−	0.0440365i
$545$	11.4034	+	5.49160i	0.488469	+	0.235234i
$546$	56.8626	−	27.3836i	2.43349	−	1.17191i
$547$	22.3203	−	27.9888i	0.954347	−	1.19671i	−0.0260455	−	0.999661i	$-0.508291\pi$
$547$	22.3203	−	27.9888i	0.954347	−	1.19671i	0.980393	−	0.197053i	$-0.0631371\pi$
$548$	−35.9182	+	28.6438i	−1.53435	+	1.22360i
$549$	5.92549	+	12.3044i	0.252894	+	0.525139i
$550$	4.00000			0.170561
$551$		0			0
$552$	−38.9706			−1.65870
$553$	2.96274	+	6.15220i	0.125989	+	0.261618i
$554$	32.6798	−	26.0612i	1.38843	−	1.10724i
$555$	−6.02095	+	7.55003i	−0.255575	+	0.320481i
$556$	48.2901	−	23.2553i	2.04796	−	0.986244i
$557$	−15.5991	−	7.51214i	−0.660956	−	0.318299i	0.0731637	−	0.997320i	$-0.476690\pi$
$557$	−15.5991	−	7.51214i	−0.660956	−	0.318299i	−0.734119	+	0.679021i	$0.762405\pi$
$558$	−42.8771	−	53.7662i	−1.81513	−	2.27610i
$559$	13.3837	+	3.05475i	0.566072	+	0.129202i
$560$	1.88815	−	8.27254i	0.0797890	−	0.349579i
$561$	−0.647690	−	0.516516i	−0.0273455	−	0.0218073i
$562$	75.2486	−	17.1750i	3.17417	−	0.724484i
$563$		−	0.757359i		−	0.0319189i	−0.999873	−	0.0159594i	$-0.994920\pi$
$563$		−	0.757359i		−	0.0319189i	0.999873	−	0.0159594i	$-0.00508026\pi$
$564$	−6.66908	−	29.2191i	−0.280819	−	1.23035i
$565$	−5.77660	+	11.9952i	−0.243023	+	0.504643i
$566$	−12.2104	+	25.3552i	−0.513242	+	1.06576i
$567$	−5.96989	−	26.1558i	−0.250712	−	1.09844i
$568$		−	38.9706i		−	1.63517i
$569$	−38.6626	+	8.82448i	−1.62082	+	0.369941i	−0.934109	−	0.356989i	$-0.883803\pi$
$569$	−38.6626	+	8.82448i	−1.62082	+	0.369941i	−0.686711	+	0.726931i	$0.740946\pi$
$570$	−27.3411	−	21.8038i	−1.14519	−	0.913260i
$571$	−3.25491	+	14.2607i	−0.136214	+	0.596791i	0.860034	+	0.510237i	$0.170442\pi$
$571$	−3.25491	+	14.2607i	−0.136214	+	0.596791i	−0.996247	+	0.0865534i	$0.972415\pi$
$572$	5.91885	+	1.35094i	0.247480	+	0.0564856i
$573$	−38.1031	−	47.7798i	−1.59178	−	1.99603i
$574$	27.5943	+	13.2887i	1.15177	+	0.554661i
$575$	13.1788	−	6.34660i	0.549596	−	0.264671i
$576$	−17.3324	+	21.7341i	−0.722183	+	0.905589i
$577$	23.2978	−	18.5794i	0.969900	−	0.773469i	−0.00410633	−	0.999992i	$-0.501307\pi$
$577$	23.2978	−	18.5794i	0.969900	−	0.773469i	0.974006	+	0.226522i	$0.0727357\pi$
$578$	−17.0884	−	35.4845i	−0.710784	−	1.47596i
$579$	12.4853			0.518871
$580$		0			0
$581$	−21.6569			−0.898478
$582$	−11.3426	−	23.5533i	−0.470168	−	0.976314i
$583$	−3.07176	+	2.44965i	−0.127219	+	0.101454i
$584$	11.0089	−	13.8047i	0.455550	−	0.571242i
$585$	9.75608	−	4.69828i	0.403364	−	0.194250i
$586$	−16.6547	−	8.02046i	−0.687998	−	0.331322i
$587$	4.77397	+	5.98637i	0.197043	+	0.247084i	0.870530	−	0.492115i	$-0.163776\pi$
$587$	4.77397	+	5.98637i	0.197043	+	0.247084i	−0.673488	+	0.739199i	$0.735204\pi$
$588$	−9.01091	−	2.05668i	−0.371604	−	0.0848161i
$589$	13.4461	−	58.9114i	0.554039	−	2.42740i
$590$	−6.90234	−	5.50443i	−0.284165	−	0.226614i
$591$	−4.70737	+	1.07443i	−0.193635	+	0.0441960i
$592$		−	12.0000i		−	0.493197i
$593$	−4.33588	−	18.9967i	−0.178053	−	0.780103i	−0.982528	−	0.186116i	$-0.940410\pi$
$593$	−4.33588	−	18.9967i	−0.178053	−	0.780103i	0.804474	−	0.593987i	$-0.202447\pi$
$594$	0.179721	−	0.373194i	0.00737402	−	0.0153123i
$595$	1.01665	−	2.11110i	0.0416787	−	0.0865467i
$596$	6.66908	+	29.2191i	0.273176	+	1.19686i
$597$			1.17157i			0.0479493i
$598$	32.9516	−	7.52098i	1.34749	−	0.307556i
$599$	−7.71672	−	6.15388i	−0.315297	−	0.251441i	0.453035	−	0.891493i	$-0.350341\pi$
$599$	−7.71672	−	6.15388i	−0.315297	−	0.251441i	−0.768332	+	0.640052i	$0.778913\pi$
$600$	−9.48549	+	41.5587i	−0.387244	+	1.69663i
$601$	−16.7410	−	3.82103i	−0.682881	−	0.155863i	−0.133013	−	0.991114i	$-0.542465\pi$
$601$	−16.7410	−	3.82103i	−0.682881	−	0.155863i	−0.549869	+	0.835251i	$0.685322\pi$
$602$	−15.2663	−	19.1434i	−0.622209	−	0.780225i
$603$	−14.4155	−	6.94214i	−0.587045	−	0.282706i
$604$	48.7804	−	23.4914i	1.98485	−	0.955851i
$605$	6.75141	−	8.46601i	0.274484	−	0.344192i
$606$	−10.6774	+	8.51491i	−0.433738	+	0.345895i
$607$	3.35302	+	6.96262i	0.136095	+	0.282604i	0.957867	−	0.287213i	$-0.0927286\pi$
$607$	3.35302	+	6.96262i	0.136095	+	0.282604i	−0.821772	+	0.569816i	$0.807014\pi$
$608$	−9.51472			−0.385873
$609$		0			0
$610$	−11.6569			−0.471972
$611$	5.38633	+	11.1848i	0.217907	+	0.452489i
$612$	7.01347	−	5.59305i	0.283503	−	0.226086i
$613$	5.61141	−	7.03648i	0.226643	−	0.284201i	−0.655488	−	0.755205i	$-0.727537\pi$
$613$	5.61141	−	7.03648i	0.226643	−	0.284201i	0.882131	+	0.471005i	$0.156108\pi$
$614$	−6.30678	+	3.03719i	−0.254521	+	0.122571i
$615$	9.75608	+	4.69828i	0.393403	+	0.189453i
$616$	−3.22442	−	4.04330i	−0.129916	−	0.162909i
$617$	−0.669085	−	0.152714i	−0.0269363	−	0.00614804i	0.209032	−	0.977909i	$-0.432969\pi$
$617$	−0.669085	−	0.152714i	−0.0269363	−	0.00614804i	−0.235968	+	0.971761i	$0.575826\pi$
$618$	6.26221	−	27.4366i	0.251903	−	1.10366i
$619$	26.2584	+	20.9404i	1.05542	+	0.841666i	0.987750	−	0.156043i	$-0.0498737\pi$
$619$	26.2584	+	20.9404i	1.05542	+	0.841666i	0.0676649	+	0.997708i	$0.478445\pi$
$620$	37.5897	−	8.57959i	1.50964	−	0.344565i
$621$		−	1.51472i		−	0.0607836i
$622$	−1.44311	−	6.32268i	−0.0578635	−	0.253516i
$623$	−15.3220	+	31.8166i	−0.613865	+	1.27470i
$624$	−12.0307	+	24.9820i	−0.481613	+	1.00008i
$625$	−2.44773	−	10.7242i	−0.0979092	−	0.428968i
$626$			23.7279i			0.948358i
$627$	−5.84957	+	1.33513i	−0.233609	+	0.0533198i
$628$	−25.3980	−	20.2542i	−1.01349	−	0.808232i
$629$	0.737370	−	3.23063i	0.0294008	−	0.128814i
$630$	−18.8295	−	4.29770i	−0.750184	−	0.171225i
$631$	22.9621	+	28.7936i	0.914109	+	1.14626i	0.988829	+	0.149052i	$0.0476220\pi$
$631$	22.9621	+	28.7936i	0.914109	+	1.14626i	−0.0747207	+	0.997204i	$0.523807\pi$
$632$	−9.60149	−	4.62384i	−0.381927	−	0.183926i
$633$	42.1644	−	20.3053i	1.67589	−	0.807064i
$634$	47.3485	−	59.3732i	1.88045	−	2.35801i
$635$	−3.39561	+	2.70791i	−0.134751	+	0.107460i
$636$	−38.0382	−	78.9871i	−1.50831	−	3.13204i
$637$	3.82843			0.151688
$638$		0			0
$639$	−24.9706			−0.987820
$640$	−8.91907	−	18.5206i	−0.352557	−	0.732092i
$641$	13.9158	−	11.0975i	0.549641	−	0.438324i	−0.308881	−	0.951101i	$-0.599954\pi$
$641$	13.9158	−	11.0975i	0.549641	−	0.438324i	0.858522	+	0.512776i	$0.171383\pi$
$642$	−53.8860	+	67.5709i	−2.12671	+	2.66681i
$643$	29.2682	−	14.0948i	1.15423	−	0.555846i	0.243926	−	0.969794i	$-0.421565\pi$
$643$	29.2682	−	14.0948i	1.15423	−	0.555846i	0.910301	+	0.413948i	$0.135850\pi$
$644$	−35.6765	−	17.1809i	−1.40585	−	0.677023i
$645$	−5.39746	−	6.76820i	−0.212525	−	0.266498i
$646$	11.6991	+	2.67025i	0.460296	+	0.105060i
$647$	8.82448	−	38.6626i	0.346926	−	1.51998i	−0.437190	−	0.899369i	$-0.644026\pi$
$647$	8.82448	−	38.6626i	0.346926	−	1.51998i	0.784117	−	0.620614i	$-0.213116\pi$
$648$	32.7353	+	26.1056i	1.28597	+	1.02552i
$649$	−1.47674	+	0.337057i	−0.0579672	+	0.0132306i
$650$		−	36.9706i		−	1.45010i
$651$	−15.3027	−	67.0454i	−0.599759	−	2.62771i
$652$	−6.52632	+	13.5520i	−0.255590	+	0.530739i
$653$	−13.0782	+	27.1571i	−0.511789	+	1.06274i	0.471698	+	0.881760i	$0.343641\pi$
$653$	−13.0782	+	27.1571i	−0.511789	+	1.06274i	−0.983487	+	0.180980i	$0.942073\pi$
$654$	16.4153	+	71.9200i	0.641888	+	2.81229i
$655$			21.3137i			0.832796i
$656$	−13.1185	+	2.99421i	−0.512191	+	0.116904i
$657$	−8.84541	−	7.05398i	−0.345092	−	0.275202i
$658$	4.92709	−	21.5870i	0.192078	−	0.841548i
$659$	14.0528	+	3.20746i	0.547420	+	0.124945i	0.487281	−	0.873245i	$-0.337989\pi$
$659$	14.0528	+	3.20746i	0.547420	+	0.124945i	0.0601386	+	0.998190i	$0.480846\pi$
$660$	−2.38699	−	2.99318i	−0.0929133	−	0.116510i
$661$	−30.0146	−	14.4543i	−1.16743	−	0.562206i	−0.253208	−	0.967412i	$-0.581486\pi$
$661$	−30.0146	−	14.4543i	−1.16743	−	0.562206i	−0.914226	+	0.405206i	$0.867200\pi$
$662$	−5.25123	+	2.52886i	−0.204095	+	0.0982869i
$663$	−4.77397	+	5.98637i	−0.185406	+	0.232491i
$664$	26.4251	−	21.0733i	1.02549	−	0.817804i
$665$	−7.36325	−	15.2899i	−0.285535	−	0.592919i
$666$	−27.3137			−1.05838
$667$		0			0
$668$	−12.1421			−0.469793
$669$	−3.32218	−	6.89859i	−0.128443	−	0.266715i
$670$	10.6774	−	8.51491i	0.412502	−	0.328960i
$671$	−1.24698	+	1.56366i	−0.0481391	+	0.0603645i
$672$	−9.75608	+	4.69828i	−0.376349	+	0.181240i
$673$	−19.4856	−	9.38378i	−0.751116	−	0.361718i	0.0188341	−	0.999823i	$-0.494005\pi$
$673$	−19.4856	−	9.38378i	−0.751116	−	0.361718i	−0.769950	+	0.638104i	$0.779719\pi$
$674$	−32.8127	−	41.1458i	−1.26390	−	1.58488i
$675$	−1.61531	−	0.368685i	−0.0621734	−	0.0141907i
$676$	1.41148	−	6.18411i	0.0542878	−	0.237850i
$677$	−17.2003	−	13.7168i	−0.661061	−	0.527179i	0.234501	−	0.972116i	$-0.424654\pi$
$677$	−17.2003	−	13.7168i	−0.661061	−	0.527179i	−0.895562	+	0.444937i	$0.853226\pi$
$678$	−75.6524	+	17.2672i	−2.90541	+	0.663142i
$679$		−	12.6863i		−	0.486855i
$680$	0.813727	+	3.56517i	0.0312050	+	0.136718i
$681$	8.52879	−	17.7102i	0.326824	−	0.678657i
$682$	4.36967	−	9.07372i	0.167323	−	0.347451i
$683$	−4.66639	−	20.4448i	−0.178554	−	0.782298i	−0.982298	−	0.187323i	$-0.940019\pi$
$683$	−4.66639	−	20.4448i	−0.178554	−	0.782298i	0.803744	−	0.594975i	$-0.202838\pi$
$684$		−	64.9706i		−	2.48421i
$685$	−11.6991	+	2.67025i	−0.447001	+	0.102025i
$686$	32.0321	+	25.5447i	1.22299	+	0.975302i
$687$	1.88815	−	8.27254i	0.0720375	−	0.315617i
$688$	10.4876	+	2.39374i	0.399838	+	0.0912604i
$689$	22.6412	+	28.3912i	0.862562	+	1.08162i
$690$	−19.2030	−	9.24767i	−0.731045	−	0.352053i
$691$	−43.2465	+	20.8264i	−1.64517	+	0.792274i	−0.645583	+	0.763690i	$0.723386\pi$
$691$	−43.2465	+	20.8264i	−1.64517	+	0.792274i	−0.999591	+	0.0285844i	$0.990900\pi$
$692$	29.4629	−	36.9453i	1.12001	−	1.40445i
$693$	−2.59076	+	2.06606i	−0.0984149	+	0.0784833i
$694$	2.60330	+	5.40581i	0.0988200	+	0.205202i
$695$	14.0000			0.531050
$696$		0			0
$697$	−3.71573			−0.140743
$698$	5.38633	+	11.1848i	0.203875	+	0.423352i
$699$	34.5673	−	27.5665i	1.30745	−	1.04266i
$700$	−27.0057	+	33.8640i	−1.02072	+	1.27994i
$701$	−36.1403	+	17.4042i	−1.36500	+	0.657349i	−0.965746	−	0.259491i	$-0.916445\pi$
$701$	−36.1403	+	17.4042i	−1.36500	+	0.657349i	−0.399254	+	0.916840i	$0.630731\pi$
$702$	−3.44929	−	1.66109i	−0.130185	−	0.0626939i
$703$	−14.9638	−	18.7640i	−0.564369	−	0.707696i
$704$	−3.96900	−	0.905898i	−0.149587	−	0.0341423i
$705$	1.74199	−	7.63215i	0.0656071	−	0.287443i
$706$	−50.9072	−	40.5971i	−1.91592	−	1.52789i
$707$	−6.46125	+	1.47474i	−0.243000	+	0.0554633i
$708$		−	33.7990i		−	1.27024i
$709$	6.48474	+	28.4115i	0.243539	+	1.06702i	0.937768	+	0.347261i	$0.112888\pi$
$709$	6.48474	+	28.4115i	0.243539	+	1.06702i	−0.694229	+	0.719754i	$0.744255\pi$
$710$	9.24767	−	19.2030i	0.347059	−	0.720675i
$711$	−2.96274	+	6.15220i	−0.111112	+	0.230726i
$712$	−12.2637	−	53.7309i	−0.459603	−	2.01365i
$713$		−	36.8284i		−	1.37924i
$714$	13.3144	−	3.03894i	0.498281	−	0.113729i
$715$	1.23982	+	0.988722i	0.0463666	+	0.0369761i
$716$	5.52484	−	24.2059i	0.206473	−	0.904618i
$717$	−46.2660	−	10.5599i	−1.72784	−	0.394367i
$718$	5.91398	+	7.41589i	0.220708	+	0.276759i
$719$	18.1474	+	8.73935i	0.676785	+	0.325923i	0.740510	−	0.672045i	$-0.234584\pi$
$719$	18.1474	+	8.73935i	0.676785	+	0.325923i	−0.0637252	+	0.997967i	$0.520298\pi$
$720$	7.64497	−	3.68163i	0.284911	−	0.137206i
$721$	8.51491	−	10.6774i	0.317112	−	0.397646i
$722$	32.0876	−	25.5890i	1.19418	−	0.952325i
$723$	19.1834	+	39.8347i	0.713438	+	1.48147i
$724$	−31.8284			−1.18289
$725$		0			0
$726$	63.1127			2.34233
$727$	0.569997	+	1.18361i	0.0211400	+	0.0438977i	0.911271	−	0.411806i	$-0.135102\pi$
$727$	0.569997	+	1.18361i	0.0211400	+	0.0438977i	−0.890131	+	0.455704i	$0.849388\pi$
$728$	−37.3708	+	29.8022i	−1.38505	+	1.10454i
$729$	14.8568	−	18.6298i	0.550251	−	0.689993i
$730$	8.70053	−	4.18995i	0.322021	−	0.155077i
$731$	2.67638	+	1.28888i	0.0989897	+	0.0476709i
$732$	−27.8247	−	34.8911i	−1.02843	−	1.28961i
$733$	40.2205	+	9.18006i	1.48558	+	0.339073i	0.886917	−	0.461929i	$-0.152843\pi$
$733$	40.2205	+	9.18006i	1.48558	+	0.339073i	0.598661	+	0.801003i	$0.295700\pi$
$734$	−9.66984	+	42.3663i	−0.356920	+	1.56377i
$735$	−1.88751	−	1.50524i	−0.0696218	−	0.0555215i
$736$	−5.65360	+	1.29040i	−0.208394	+	0.0475647i
$737$		−	2.34315i		−	0.0863109i
$738$	6.81524	+	29.8595i	0.250873	+	1.09914i
$739$	−1.76637	+	3.66791i	−0.0649770	+	0.134926i	−0.930928	−	0.365203i	$-0.881000\pi$
$739$	−1.76637	+	3.66791i	−0.0649770	+	0.134926i	0.865951	+	0.500129i	$0.166714\pi$
$740$	6.64437	−	13.7972i	0.244252	−	0.507194i
$741$	12.3401	+	54.0655i	0.453324	+	1.98614i
$742$		−	64.7696i		−	2.37777i
$743$	23.0637	−	5.26415i	0.846126	−	0.193123i	0.222585	−	0.974913i	$-0.428551\pi$
$743$	23.0637	−	5.26415i	0.846126	−	0.193123i	0.623541	+	0.781791i	$0.285693\pi$
$744$	83.9108	+	66.9166i	3.07632	+	2.45328i
$745$	−1.74199	+	7.63215i	−0.0638215	+	0.279620i
$746$	61.9342	+	14.1361i	2.26757	+	0.517558i
$747$	−13.5028	−	16.9320i	−0.494043	−	0.619510i
$748$	1.18361	+	0.569997i	0.0432771	+	0.0208411i
$749$	−37.7876	+	18.1976i	−1.38073	+	0.664925i
$750$	−32.7057	+	41.0116i	−1.19424	+	1.49753i
$751$	−19.7911	+	15.7828i	−0.722186	+	0.575924i	−0.914101	−	0.405488i	$-0.867102\pi$
$751$	−19.7911	+	15.7828i	−0.722186	+	0.575924i	0.191915	+	0.981412i	$0.438530\pi$
$752$	4.22079	+	8.76455i	0.153916	+	0.319610i
$753$	−48.4558			−1.76583
$754$		0			0
$755$	14.1421			0.514685
$756$	1.94609	+	4.04110i	0.0707786	+	0.146973i
$757$	19.9482	−	15.9082i	0.725030	−	0.578192i	−0.189901	−	0.981803i	$-0.560817\pi$
$757$	19.9482	−	15.9082i	0.725030	−	0.578192i	0.914931	+	0.403611i	$0.132245\pi$
$758$	−10.4924	+	13.1570i	−0.381099	+	0.477884i
$759$	−3.29471	+	1.58665i	−0.119590	+	0.0575917i
$760$	23.8624	+	11.4915i	0.865581	+	0.416842i
$761$	28.4299	+	35.6499i	1.03058	+	1.29231i	0.955456	+	0.295135i	$0.0953647\pi$
$761$	28.4299	+	35.6499i	1.03058	+	1.29231i	0.0751267	+	0.997174i	$0.476064\pi$
$762$	−24.6790	−	5.63283i	−0.894027	−	0.204056i
$763$	−7.96602	+	34.9014i	−0.288389	+	1.26352i
$764$	75.7686	+	60.4234i	2.74121	+	2.18604i
$765$	2.28440	−	0.521399i	0.0825926	−	0.0188512i
$766$			8.48528i			0.306586i
$767$	3.11529	+	13.6490i	0.112487	+	0.492836i
$768$	31.3938	−	65.1899i	1.13283	−	2.35234i
$769$	−21.3092	+	44.2490i	−0.768429	+	1.59566i	0.0343686	+	0.999409i	$0.489058\pi$
$769$	−21.3092	+	44.2490i	−0.768429	+	1.59566i	−0.802798	+	0.596251i	$0.796656\pi$
$770$	−0.629384	−	2.75751i	−0.0226814	−	0.0993739i
$771$			43.8701i			1.57994i
$772$	−19.3026	+	4.40569i	−0.694715	+	0.158564i
$773$	15.2572	+	12.1672i	0.548764	+	0.437625i	0.858215	−	0.513291i	$-0.171574\pi$
$773$	15.2572	+	12.1672i	0.548764	+	0.437625i	−0.309451	+	0.950915i	$0.600145\pi$
$774$	5.44849	−	23.8714i	0.195842	−	0.858039i
$775$	−39.2743	−	8.96409i	−1.41077	−	0.322000i
$776$	12.3445	+	15.4795i	0.443141	+	0.555681i
$777$	−24.6088	−	11.8510i	−0.882836	−	0.425151i
$778$	6.58942	−	3.17330i	0.236242	−	0.113768i
$779$	−16.7792	+	21.0404i	−0.601176	+	0.753851i
$780$	−27.6649	+	22.0620i	−0.990563	+	0.789948i
$781$	−1.58665	−	3.29471i	−0.0567748	−	0.117894i
$782$	7.31371			0.261538
$783$		0			0
$784$	3.00000			0.107143
$785$	−3.68163	−	7.64497i	−0.131403	−	0.272861i
$786$	−97.1233	+	77.4533i	−3.46427	+	2.76267i
$787$	33.7204	−	42.2840i	1.20200	−	1.50726i	0.392912	−	0.919576i	$-0.371468\pi$
$787$	33.7204	−	42.2840i	1.20200	−	1.50726i	0.809090	−	0.587685i	$-0.199961\pi$
$788$	6.89859	−	3.32218i	0.245752	−	0.118348i
$789$	5.99762	+	2.88830i	0.213521	+	0.102826i
$790$	−3.63396	−	4.55685i	−0.129291	−	0.162125i
$791$	−36.7127	−	8.37944i	−1.30535	−	0.297939i
$792$	1.15078	−	5.04191i	0.0408913	−	0.179156i
$793$	14.4524	+	11.5254i	0.513219	+	0.409278i
$794$	45.5277	−	10.3914i	1.61572	−	0.368777i
$795$		−	22.8995i		−	0.812161i
$796$	−0.413414	−	1.81128i	−0.0146531	−	0.0641993i
$797$	−22.4492	+	46.6162i	−0.795191	+	1.65123i	−0.0368972	+	0.999319i	$0.511747\pi$
$797$	−22.4492	+	46.6162i	−0.795191	+	1.65123i	−0.758294	+	0.651913i	$0.773967\pi$
$798$	42.9162	−	89.1164i	1.51922	−	3.15468i
$799$	0.597756	+	2.61894i	0.0211471	+	0.0926515i
$800$			6.34315i			0.224264i
$801$	−34.4283	+	7.85804i	−1.21646	+	0.277650i
$802$	−35.2150	−	28.0830i	−1.24348	−	0.991645i
$803$	0.368685	−	1.61531i	0.0130106	−	0.0570032i
$804$	50.9734	+	11.6343i	1.79769	+	0.410312i
$805$	−6.44885	−	8.08660i	−0.227292	−	0.285015i
$806$	−83.8651	−	40.3873i	−2.95402	−	1.42258i
$807$	−68.4206	+	32.9496i	−2.40852	+	1.15988i
$808$	6.44885	−	8.08660i	0.226870	−	0.284485i
$809$	−28.3682	+	22.6229i	−0.997372	+	0.795378i	−0.978877	−	0.204451i	$-0.934459\pi$
$809$	−28.3682	+	22.6229i	−0.997372	+	0.795378i	−0.0184955	+	0.999829i	$0.505888\pi$
$810$	9.93572	+	20.6317i	0.349106	+	0.724925i
$811$	−10.8284			−0.380238			−0.190119	−	0.981761i	$-0.560887\pi$
$811$	−10.8284			−0.380238			−0.190119	+	0.981761i	$0.560887\pi$
$812$		0			0
$813$	39.9706			1.40183
$814$	−1.73553	−	3.60388i	−0.0608305	−	0.126316i
$815$	−3.07176	+	2.44965i	−0.107599	+	0.0858075i
$816$	−3.74094	+	4.69099i	−0.130959	+	0.164217i
$817$	19.3841	−	9.33489i	0.678164	−	0.326586i
$818$	41.2635	+	19.8714i	1.44274	+	0.694789i
$819$	19.0959	+	23.9455i	0.667264	+	0.836723i
$820$	−16.7410	−	3.82103i	−0.584623	−	0.133436i
$821$	−0.330506	+	1.44804i	−0.0115347	+	0.0505370i	−0.980368	−	0.197178i	$-0.936822\pi$
$821$	−0.330506	+	1.44804i	−0.0115347	+	0.0505370i	0.968833	+	0.247715i	$0.0796796\pi$
$822$	−54.6822	−	43.6076i	−1.90726	−	1.52099i
$823$	52.9233	−	12.0794i	1.84479	−	0.421061i	0.850335	−	0.526241i	$-0.176399\pi$
$823$	52.9233	−	12.0794i	1.84479	−	0.421061i	0.994453	+	0.105180i	$0.0335419\pi$
$824$			21.3137i			0.742498i
$825$	0.890084	+	3.89971i	0.0309887	+	0.135771i
$826$	10.8343	−	22.4977i	0.376974	−	0.782795i
$827$	14.2746	−	29.6414i	0.496375	−	1.03073i	−0.490827	−	0.871257i	$-0.663305\pi$
$827$	14.2746	−	29.6414i	0.496375	−	1.03073i	0.987202	−	0.159476i	$-0.0509805\pi$
$828$	−8.81138	−	38.6052i	−0.306217	−	1.34162i
$829$			29.7990i			1.03496i	0.855695	+	0.517481i	$0.173130\pi$
$829$			29.7990i			1.03496i	−0.855695	+	0.517481i	$0.826870\pi$
$830$	18.0218	−	4.11336i	0.625546	−	0.142777i
$831$	32.6798	+	26.0612i	1.13365	+	0.904055i
$832$	−8.37289	+	36.6840i	−0.290278	+	1.27179i
$833$	0.807657	+	0.184342i	0.0279836	+	0.00638708i
$834$	50.8755	+	63.7959i	1.76167	+	2.20907i
$835$	−2.85749	−	1.37609i	−0.0988875	−	0.0476217i
$836$	8.57247	−	4.12828i	0.296485	−	0.142780i
$837$	−2.60093	+	3.26147i	−0.0899014	+	0.112733i
$838$	−17.9591	+	14.3219i	−0.620387	+	0.494742i
$839$	3.44023	+	7.14372i	0.118770	+	0.246629i	0.951875	−	0.306486i	$-0.0991533\pi$
$839$	3.44023	+	7.14372i	0.118770	+	0.246629i	−0.833105	+	0.553115i	$0.813439\pi$
$840$	30.1421			1.04000
$841$		0			0
$842$	−89.5980			−3.08775
$843$	33.4888	+	69.5402i	1.15341	+	2.39509i
$844$	−58.0222	+	46.2712i	−1.99721	+	1.59272i
$845$	1.03303	−	1.29538i	0.0355374	−	0.0445625i
$846$	19.9494	−	9.60711i	0.685874	−	0.330299i
$847$	27.5943	+	13.2887i	0.948153	+	0.456606i
$848$	17.7419	+	22.2477i	0.609260	+	0.763988i
$849$	−27.4366	−	6.26221i	−0.941620	−	0.214919i
$850$	1.78017	−	7.79942i	0.0610592	−	0.267518i
$851$	−11.4362	−	9.12005i	−0.392027	−	0.312631i
$852$	79.5521	−	18.1573i	2.72541	−	0.622057i
$853$		−	22.9706i		−	0.786497i	−0.919432	−	0.393249i	$-0.871351\pi$
$853$		−	22.9706i		−	0.786497i	0.919432	−	0.393249i	$-0.128649\pi$
$854$	−7.33664	−	32.1439i	−0.251055	−	1.09994i
$855$	7.36325	−	15.2899i	0.251818	−	0.522905i
$856$	28.4002	−	58.9737i	0.970700	−	2.01568i
$857$	1.37330	+	6.01684i	0.0469112	+	0.205531i	0.992952	−	0.118516i	$-0.0378136\pi$
$857$	1.37330	+	6.01684i	0.0469112	+	0.205531i	−0.946041	+	0.324047i	$0.894956\pi$
$858$			9.24264i			0.315539i
$859$	19.2333	−	4.38988i	0.656232	−	0.149781i	0.118576	−	0.992945i	$-0.462167\pi$
$859$	19.2333	−	4.38988i	0.656232	−	0.149781i	0.537656	+	0.843164i	$0.319310\pi$
$860$	10.7329	+	8.55922i	0.365990	+	0.291867i
$861$	−6.81524	+	29.8595i	−0.232263	+	1.01761i
$862$	−46.2660	−	10.5599i	−1.57583	−	0.359672i
$863$	−10.6696	−	13.3792i	−0.363197	−	0.455435i	0.566335	−	0.824175i	$-0.308361\pi$
$863$	−10.6696	−	13.3792i	−0.363197	−	0.455435i	−0.929533	+	0.368740i	$0.879789\pi$
$864$	0.591805	+	0.284998i	0.0201336	+	0.00969584i
$865$	11.1208	−	5.35549i	0.378118	−	0.182092i
$866$	−46.1015	+	57.8095i	−1.56659	+	1.96445i
$867$	30.7923	−	24.5560i	1.04576	−	0.833966i
$868$	47.3167	+	98.2541i	1.60603	+	3.33496i
$869$	−1.00000			−0.0339227
$870$		0			0
$871$	−21.6569			−0.733815
$872$	−24.2411	−	50.3372i	−0.820908	−	1.70463i
$873$	9.91854	−	7.90977i	0.335692	−	0.267705i
$874$	33.0266	−	41.4141i	1.11714	−	1.40085i
$875$	−22.9349	+	11.0449i	−0.775342	+	0.373385i
$876$	33.3093	+	16.0409i	1.12542	+	0.541973i
$877$	−23.1577	−	29.0389i	−0.781981	−	0.980574i	−0.999989	−	0.00462667i	$-0.998527\pi$
$877$	−23.1577	−	29.0389i	−0.781981	−	0.980574i	0.218008	−	0.975947i	$-0.430044\pi$
$878$	−0.807657	−	0.184342i	−0.0272571	−	0.00622125i
$879$	4.11336	−	18.0218i	0.138740	−	0.607861i
$880$	0.971536	+	0.774774i	0.0327505	+	0.0261176i
$881$	−13.6490	+	3.11529i	−0.459846	+	0.104957i	−0.446167	−	0.894950i	$-0.647211\pi$
$881$	−13.6490	+	3.11529i	−0.459846	+	0.104957i	−0.0136788	+	0.999906i	$0.504354\pi$
$882$		−	6.82843i		−	0.229925i
$883$	8.55068	+	37.4630i	0.287753	+	1.26073i	0.887600	+	0.460615i	$0.152371\pi$
$883$	8.55068	+	37.4630i	0.287753	+	1.26073i	−0.599847	+	0.800115i	$0.704772\pi$
$884$	5.26828	−	10.9397i	0.177191	−	0.367941i
$885$	3.83051	−	7.95414i	0.128761	−	0.267375i
$886$	−13.0775	−	57.2961i	−0.439346	−	1.92490i
$887$		−	17.1005i		−	0.574179i	−0.957904	−	0.287089i	$-0.907312\pi$
$887$		−	17.1005i		−	0.574179i	0.957904	−	0.287089i	$-0.0926877\pi$
$888$	41.5587	−	9.48549i	1.39462	−	0.318312i
$889$	−9.60423	−	7.65912i	−0.322116	−	0.256879i
$890$	6.70726	−	29.3864i	0.224828	−	0.985035i
$891$	3.83043	+	0.874270i	0.128324	+	0.0292891i
$892$	7.57050	+	9.49310i	0.253479	+	0.317853i
$893$	17.5291	+	8.44157i	0.586589	+	0.282487i
$894$	−41.1089	+	19.7970i	−1.37489	+	0.662111i
$895$	4.04351	−	5.07040i	0.135160	−	0.169485i
$896$	45.4574	−	36.2510i	1.51862	−	1.21106i
$897$	14.6648	+	30.4518i	0.489644	+	1.01676i
$898$	−84.4264			−2.81735
$899$		0			0
$900$	−43.3137			−1.44379
$901$	3.40940	+	7.07969i	0.113584	+	0.235859i
$902$	−3.50673	+	2.79653i	−0.116761	+	0.0931142i
$903$	15.2663	−	19.1434i	0.508031	−	0.637051i
$904$	52.9495	−	25.4992i	1.76108	−	0.848089i
$905$	−7.49039	−	3.60718i	−0.248989	−	0.119907i
$906$	51.3920	+	64.4436i	1.70739	+	2.14099i
$907$	−21.7256	−	4.95872i	−0.721385	−	0.164651i	−0.153961	−	0.988077i	$-0.549203\pi$
$907$	−21.7256	−	4.95872i	−0.721385	−	0.164651i	−0.567424	+	0.823425i	$0.692060\pi$
$908$	−6.93633	+	30.3900i	−0.230190	+	1.00853i
$909$	−5.18152	−	4.13213i	−0.171860	−	0.137054i
$910$	−25.4867	+	5.81717i	−0.844876	+	0.192837i
$911$		−	15.4437i		−	0.511671i	−0.966720	−	0.255835i	$-0.917649\pi$
$911$		−	15.4437i		−	0.511671i	0.966720	−	0.255835i	$-0.0823505\pi$
$912$	9.66984	+	42.3663i	0.320200	+	1.40289i
$913$	1.37609	−	2.85749i	0.0455421	−	0.0945691i
$914$	−1.07832	+	2.23916i	−0.0356678	+	0.0740649i
$915$	−2.59389	−	11.3646i	−0.0857515	−	0.375702i
$916$			13.4558i			0.444594i
$917$	−58.7728	+	13.4145i	−1.94085	+	0.442986i
$918$	−0.647690	−	0.516516i	−0.0213770	−	0.0170476i
$919$	−1.81180	+	7.93800i	−0.0597656	+	0.261850i	−0.995980	−	0.0895801i	$-0.971447\pi$
$919$	−1.81180	+	7.93800i	−0.0597656	+	0.261850i	0.936214	+	0.351430i	$0.114305\pi$
$920$	15.7374	+	3.59196i	0.518847	+	0.118424i
$921$	−4.36443	−	5.47282i	−0.143813	−	0.180336i
$922$	30.4518	+	14.6648i	1.00288	+	0.482961i
$923$	−30.4518	+	14.6648i	−1.00233	+	0.482699i
$924$	6.75141	−	8.46601i	0.222105	−	0.278511i
$925$	−12.5093	+	9.97584i	−0.411303	+	0.328003i
$926$	−27.2347	−	56.5534i	−0.894987	−	1.85846i
$927$	13.6569			0.448550
$928$		0			0
$929$	18.6863			0.613077			0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863			0.613077			0.306539	+	0.951858i	$0.400829\pi$
$930$	25.4683	+	52.8855i	0.835139	+	1.73418i
$931$	4.69099	−	3.74094i	0.153741	−	0.122604i
$932$	−43.7146	+	54.8163i	−1.43192	+	1.79557i
$933$	5.84304	−	2.81386i	0.191292	−	0.0921216i
$934$	83.4279	+	40.1768i	2.72984	+	1.31462i
$935$	0.213948	+	0.268282i	0.00699684	+	0.00877376i
$936$	−46.6006	−	10.6363i	−1.52319	−	0.347658i
$937$	−3.69995	+	16.2105i	−0.120872	+	0.529575i	0.877845	+	0.478944i	$0.158980\pi$
$937$	−3.69995	+	16.2105i	−0.120872	+	0.529575i	−0.998717	+	0.0506309i	$0.983877\pi$
$938$	30.2001	+	24.0838i	0.986069	+	0.786364i
$939$	−23.1330	+	5.27996i	−0.754917	+	0.172305i
$940$			12.4142i			0.404907i
$941$	−12.5942	−	55.1790i	−0.410560	−	1.79878i	−0.581551	−	0.813510i	$-0.697554\pi$
$941$	−12.5942	−	55.1790i	−0.410560	−	1.79878i	0.170991	−	0.985273i	$-0.445303\pi$
$942$	21.4581	−	44.5582i	0.699142	−	1.45178i
$943$	−7.11657	+	14.7777i	−0.231747	+	0.481228i
$944$	2.44118	+	10.6955i	0.0794536	+	0.348109i
$945$			1.17157i			0.0381113i
$946$	3.49588	−	0.797913i	0.113661	−	0.0259424i
$947$	−2.04466	−	1.63057i	−0.0664427	−	0.0529863i	0.589705	−	0.807618i	$-0.299244\pi$
$947$	−2.04466	−	1.63057i	−0.0664427	−	0.0529863i	−0.656148	+	0.754632i	$0.727815\pi$
$948$	4.96527	−	21.7543i	0.161264	−	0.706545i
$949$	−14.9298	−	3.40762i	−0.484641	−	0.110616i
$950$	−36.1257	−	45.3002i	−1.17207	−	1.46973i
$951$	68.4206	+	32.9496i	2.21869	+	1.06846i
$952$	−9.31885	+	4.48772i	−0.302026	+	0.145448i
$953$	−22.2133	+	27.8546i	−0.719560	+	0.902300i	−0.998313	−	0.0580628i	$-0.981508\pi$
$953$	−22.2133	+	27.8546i	−0.719560	+	0.902300i	0.278753	+	0.960363i	$0.410079\pi$
$954$	50.6389	−	40.3832i	1.63949	−	1.30745i
$955$	10.9832	+	22.8069i	0.355408	+	0.738013i
$956$	75.2548			2.43392
$957$		0			0
$958$	−16.6569			−0.538159
$959$	−14.7265	−	30.5799i	−0.475544	−	0.987476i
$960$	18.5512	−	14.7941i	0.598739	−	0.477478i
$961$	−43.9101	+	55.0616i	−1.41646	+	1.77618i
$962$	−33.3093	+	16.0409i	−1.07394	+	0.517180i
$963$	−37.7876	−	18.1976i	−1.21769	−	0.586409i
$964$	−43.7146	−	54.8163i	−1.40795	−	1.76551i
$965$	−5.04191	−	1.15078i	−0.162305	−	0.0370450i
$966$	13.4145	−	58.7728i	0.431605	−	1.89098i
$967$	−27.5538	−	21.9734i	−0.886071	−	0.706618i	0.0706887	−	0.997498i	$-0.477480\pi$
$967$	−27.5538	−	21.9734i	−0.886071	−	0.706618i	−0.956759	+	0.290881i	$0.906052\pi$
$968$	−46.6006	+	10.6363i	−1.49780	+	0.341863i
$969$			12.0000i			0.385496i
$970$	2.40955	+	10.5569i	0.0773660	+	0.338963i
$971$	6.79325	−	14.1063i	0.218006	−	0.452694i	−0.763070	−	0.646315i	$-0.776309\pi$
$971$	6.79325	−	14.1063i	0.218006	−	0.452694i	0.981076	+	0.193621i	$0.0620233\pi$
$972$	−35.9740	+	74.7008i	−1.15387	+	2.39603i
$973$	8.81138	+	38.6052i	0.282480	+	1.23763i
$974$		−	27.7990i		−	0.890737i
$975$	36.0436	−	8.22672i	1.15432	−	0.263466i
$976$	11.3250	+	9.03143i	0.362506	+	0.289089i
$977$	−8.04893	+	35.2647i	−0.257508	+	1.12822i	0.666398	+	0.745597i	$0.267835\pi$
$977$	−8.04893	+	35.2647i	−0.257508	+	1.12822i	−0.923906	+	0.382620i	$0.875022\pi$
$978$	−22.3254	−	5.09562i	−0.713886	−	0.162940i
$979$	−3.22442	−	4.04330i	−0.103053	−	0.129224i
$980$	3.44929	+	1.66109i	0.110184	+	0.0530616i
$981$	−32.2538	+	15.5326i	−1.02978	+	0.495918i
$982$	31.9752	−	40.0957i	1.02037	−	1.27950i
$983$	17.0987	−	13.6358i	0.545364	−	0.434913i	−0.311657	−	0.950195i	$-0.600884\pi$
$983$	17.0987	−	13.6358i	0.545364	−	0.434913i	0.857021	+	0.515281i	$0.172313\pi$
$984$	−20.7392	−	43.0654i	−0.661142	−	1.37287i
$985$	2.00000			0.0637253
$986$		0			0
$987$	22.1421			0.704792
$988$	−38.1562	−	79.2322i	−1.21391	−	2.52071i
$989$	10.2519	−	8.17563i	0.325992	−	0.259970i
$990$	1.76350	−	2.21135i	0.0560476	−	0.0702814i
$991$	−11.5580	+	5.56605i	−0.367152	+	0.176811i	−0.608358	−	0.793663i	$-0.708171\pi$
$991$	−11.5580	+	5.56605i	−0.367152	+	0.176811i	0.241206	+	0.970474i	$0.422457\pi$
$992$	14.3890	+	6.92937i	0.456851	+	0.220008i
$993$	−3.63396	−	4.55685i	−0.115320	−	0.144607i
$994$	58.7728	+	13.4145i	1.86416	+	0.425482i
$995$	0.107985	−	0.473114i	0.00342336	−	0.0149987i
$996$	55.3299	+	44.1241i	1.75319	+	1.39813i
$997$	−27.5751	+	6.29384i	−0.873313	+	0.199328i	−0.635610	−	0.772010i	$-0.719252\pi$
$997$	−27.5751	+	6.29384i	−0.873313	+	0.199328i	−0.237703	+	0.971338i	$0.576394\pi$
$998$		−	45.7990i		−	1.44974i
$999$	0.368685	+	1.61531i	0.0116647	+	0.0511063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.k.270.1		24
29.2	odd	28		841.2.d.f.645.1		12
29.3	odd	28		841.2.d.f.574.2		12
29.4	even	14		841.2.b.a.840.1		4
29.5	even	14	inner	841.2.e.k.196.1		24
29.6	even	14	inner	841.2.e.k.63.4		24
29.7	even	7	inner	841.2.e.k.267.4		24
29.8	odd	28		841.2.d.j.605.2		12
29.9	even	14	inner	841.2.e.k.236.4		24
29.10	odd	28		29.2.a.a.1.1	✓	2
29.11	odd	28		841.2.d.f.190.1		12
29.12	odd	4		841.2.d.j.571.2		12
29.13	even	14	inner	841.2.e.k.651.1		24
29.14	odd	28		841.2.d.f.778.2		12
29.15	odd	28		841.2.d.j.778.1		12
29.16	even	7	inner	841.2.e.k.651.4		24
29.17	odd	4		841.2.d.f.571.1		12
29.18	odd	28		841.2.d.j.190.2		12
29.19	odd	28		841.2.a.d.1.2		2
29.20	even	7	inner	841.2.e.k.236.1		24
29.21	odd	28		841.2.d.f.605.1		12
29.22	even	14	inner	841.2.e.k.267.1		24
29.23	even	7	inner	841.2.e.k.63.1		24
29.24	even	7	inner	841.2.e.k.196.4		24
29.25	even	7		841.2.b.a.840.4		4
29.26	odd	28		841.2.d.j.574.1		12
29.27	odd	28		841.2.d.j.645.2		12
29.28	even	2	inner	841.2.e.k.270.4		24
87.68	even	28		261.2.a.d.1.2		2
87.77	even	28		7569.2.a.c.1.1		2
116.39	even	28		464.2.a.h.1.1		2
145.39	odd	28		725.2.a.b.1.2		2
145.68	even	28		725.2.b.b.349.4		4
145.97	even	28		725.2.b.b.349.1		4
203.97	even	28		1421.2.a.j.1.1		2
232.155	even	28		1856.2.a.w.1.2		2
232.213	odd	28		1856.2.a.r.1.1		2
319.10	even	28		3509.2.a.j.1.2		2
348.155	odd	28		4176.2.a.bq.1.2		2
377.155	odd	28		4901.2.a.g.1.2		2
435.329	even	28		6525.2.a.o.1.1		2
493.271	odd	28		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.10	odd	28
261.2.a.d.1.2		2	87.68	even	28
464.2.a.h.1.1		2	116.39	even	28
725.2.a.b.1.2		2	145.39	odd	28
725.2.b.b.349.1		4	145.97	even	28
725.2.b.b.349.4		4	145.68	even	28
841.2.a.d.1.2		2	29.19	odd	28
841.2.b.a.840.1		4	29.4	even	14
841.2.b.a.840.4		4	29.25	even	7
841.2.d.f.190.1		12	29.11	odd	28
841.2.d.f.571.1		12	29.17	odd	4
841.2.d.f.574.2		12	29.3	odd	28
841.2.d.f.605.1		12	29.21	odd	28
841.2.d.f.645.1		12	29.2	odd	28
841.2.d.f.778.2		12	29.14	odd	28
841.2.d.j.190.2		12	29.18	odd	28
841.2.d.j.571.2		12	29.12	odd	4
841.2.d.j.574.1		12	29.26	odd	28
841.2.d.j.605.2		12	29.8	odd	28
841.2.d.j.645.2		12	29.27	odd	28
841.2.d.j.778.1		12	29.15	odd	28
841.2.e.k.63.1		24	29.23	even	7	inner
841.2.e.k.63.4		24	29.6	even	14	inner
841.2.e.k.196.1		24	29.5	even	14	inner
841.2.e.k.196.4		24	29.24	even	7	inner
841.2.e.k.236.1		24	29.20	even	7	inner
841.2.e.k.236.4		24	29.9	even	14	inner
841.2.e.k.267.1		24	29.22	even	14	inner
841.2.e.k.267.4		24	29.7	even	7	inner
841.2.e.k.270.1		24	1.1	even	1	trivial
841.2.e.k.270.4		24	29.28	even	2	inner
841.2.e.k.651.1		24	29.13	even	14	inner
841.2.e.k.651.4		24	29.16	even	7	inner
1421.2.a.j.1.1		2	203.97	even	28
1856.2.a.r.1.1		2	232.213	odd	28
1856.2.a.w.1.2		2	232.155	even	28
3509.2.a.j.1.2		2	319.10	even	28
4176.2.a.bq.1.2		2	348.155	odd	28
4901.2.a.g.1.2		2	377.155	odd	28
6525.2.a.o.1.1		2	435.329	even	28
7569.2.a.c.1.1		2	87.77	even	28
8381.2.a.e.1.1		2	493.271	odd	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.04749 - 2.17513i) q^{2} +(1.88751 - 1.50524i) q^{3} +(-2.38699 + 2.99318i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-5.25123 - 2.52886i) q^{6} +(-1.76350 - 2.21135i) q^{7} +(4.30354 + 0.982255i) q^{8} +(0.629384 - 2.75751i) q^{9} +O(q^{10})\)	\(q+(-1.04749 - 2.17513i) q^{2} +(1.88751 - 1.50524i) q^{3} +(-2.38699 + 2.99318i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-5.25123 - 2.52886i) q^{6} +(-1.76350 - 2.21135i) q^{7} +(4.30354 + 0.982255i) q^{8} +(0.629384 - 2.75751i) q^{9} +(1.88751 + 1.50524i) q^{10} +(0.403828 - 0.0921712i) q^{11} +9.24264i q^{12} +(-0.851905 - 3.73244i) q^{13} +(-2.96274 + 6.15220i) q^{14} +(-1.04749 + 2.17513i) q^{15} +(-0.667563 - 2.92478i) q^{16} -0.828427i q^{17} +(-6.65722 + 1.51947i) q^{18} +(-4.69099 - 3.74094i) q^{19} +(0.851905 - 3.73244i) q^{20} +(-6.65722 - 1.51947i) q^{21} +(-0.623490 - 0.781831i) q^{22} +(-3.29471 - 1.58665i) q^{23} +(9.60149 - 4.62384i) q^{24} +(-2.49396 + 3.12733i) q^{25} +(-7.22619 + 5.76269i) q^{26} +(0.179721 + 0.373194i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(4.36967 + 9.07372i) q^{31} +(1.23982 - 0.988722i) q^{32} +(0.623490 - 0.781831i) q^{33} +(-1.80194 + 0.867767i) q^{34} +(2.54832 + 1.22721i) q^{35} +(6.75141 + 8.46601i) q^{36} +(3.89971 + 0.890084i) q^{37} +(-3.22328 + 14.1221i) q^{38} +(-7.22619 - 5.76269i) q^{39} +(-4.30354 + 0.982255i) q^{40} -4.48528i q^{41} +(3.66832 + 16.0720i) q^{42} +(-1.55581 + 3.23068i) q^{43} +(-0.688047 + 1.42874i) q^{44} +(0.629384 + 2.75751i) q^{45} +8.82843i q^{46} +(-3.16134 + 0.721555i) q^{47} +(-5.66252 - 4.51571i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(9.41474 + 2.14885i) q^{50} +(-1.24698 - 1.56366i) q^{51} +(13.2054 + 6.35937i) q^{52} +(-8.54594 + 4.11551i) q^{53} +(0.623490 - 0.781831i) q^{54} +(-0.323845 + 0.258258i) q^{55} +(-5.41716 - 11.2488i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(-4.01023 - 8.32733i) q^{60} +(-3.77502 + 3.01048i) q^{61} +(15.1593 - 19.0092i) q^{62} +(-7.20775 + 3.47107i) q^{63} +(-8.85511 - 4.26439i) q^{64} +(2.38699 + 2.99318i) q^{65} +(-2.35368 - 0.537213i) q^{66} +(1.25877 - 5.51503i) q^{67} +(2.47964 + 1.97744i) q^{68} +(-8.60708 + 1.96451i) q^{69} -6.82843i q^{70} +(-1.96451 - 8.60708i) q^{71} +(5.41716 - 11.2488i) q^{72} +(1.73553 - 3.60388i) q^{73} +(-2.14885 - 9.41474i) q^{74} +9.65685i q^{75} +(22.3946 - 5.11143i) q^{76} +(-0.915973 - 0.730464i) q^{77} +(-4.96527 + 21.7543i) q^{78} +(-2.35368 - 0.537213i) q^{79} +(1.87047 + 2.34549i) q^{80} +(8.54594 + 4.11551i) q^{81} +(-9.75608 + 4.69828i) q^{82} +(4.77397 - 5.98637i) q^{83} +(20.4387 - 16.2994i) q^{84} +(0.359441 + 0.746387i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(-5.41716 - 11.2488i) q^{89} +(5.33868 - 4.25745i) q^{90} +(-6.75141 + 8.46601i) q^{91} +(12.6136 - 6.07437i) q^{92} +(21.9059 + 10.5493i) q^{93} +(4.88094 + 6.12051i) q^{94} +(5.84957 + 1.33513i) q^{95} +(0.851905 - 3.73244i) q^{96} +(3.50673 + 2.79653i) q^{97} +(2.35368 - 0.537213i) q^{98} -1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

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